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Masters Degrees (Stochastics)

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High-level training in statistics and the modelling of random processes for applications in science, business or health care. Read more
High-level training in statistics and the modelling of random processes for applications in science, business or health care.

For many complex systems in nature and society, stochastics can be used to efficiently describe the randomness present in all these systems, thereby giving the data greater explanatory and predictive power. Examples include statistical mechanics, financial markets, mobile phone networks, and operations research problems. The Master’s specialisation in Applied Stochastics will train you to become a mathematician that can help both scientists and businessmen make better decisions, conclusions and predictions. You’ll be able to bring clarity to the accumulating information overload they receive.

The members of the Applied Stochastics group have ample experience with the pure mathematical side of stochastics. This area provides powerful techniques in functional analysis, partial differential equations, geometry of metric spaces and number theory, for example. The group also often gives advice to both their academic colleagues, and organisations outside of academia. They will therefore not only be able to teach you the theoretical basis you need to solve real world stochastics problems, but also to help you develop the communications skills and professional expertise to cooperate with people from outside of mathematics.

See the website http://www.ru.nl/masters/mathematics/stochastics

Why study Applied Stochastics at Radboud University?

- This specialisation focuses both on theoretical and applied topics. It’s your choice whether you want to specialise in pure theoretical research or perform an internship in a company setting.
- Mathematicians at Radboud University are expanding their knowledge of random graphs and networks, which can be applied in the ever-growing fields of distribution systems, mobile phone networks and social networks.
- In a unique and interesting collaboration with Radboudumc, stochastics students can help researchers at the hospital with very challenging statistical questions.
- Because the Netherlands is known for its expertise in the field of stochastics, it offers a great atmosphere to study this field. And with the existence of the Mastermath programme, you can follow the best mathematics courses in the country, regardless of the university that offers them.
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that you’ll get plenty of one-on-one time with your thesis supervisor at Radboud University .
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating.

Career prospects

Master's programme in Mathematics

Mathematicians are needed in all industries, including the banking, technology and service industries, to name a few. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad and is the reason why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

PhD positions

Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.

Our research in this field

The research of members of the Applied Stochastics Department, focuses on combinatorics, (quantum) probability and mathematical statistics. Below, a small sample of the research our members pursue.

Eric Cator’s research has two main themes, probability and statistics.
1. In probability, he works on interacting particles systems, random polymers and last passage percolation. He has also recently begun working on epidemic models on finite graphs.
2. In statistics, he works on problems arising in mathematical statistics, for example in deconvolution problems, the CAR assumption and more recently on the local minimax property of least squares estimators.

Cator also works on more applied problems, usually in collaboration with people from outside statistics, for example on case reserving for insurance companies or airplane maintenance. He has a history of changing subjects: “I like to work on any problem that takes my fancy, so this description might be outdated very quickly!”

Hans Maassen researches quantum probability or non-commutative probability, which concerns a generalisation of probability theory that is broad enough to contain quantum mechanics. He takes part in the Geometry and Quantum Theory (GQT) research cluster of connected universities in the Netherlands. In collaboration with Burkhard Kümmerer he is also developing the theory of quantum Markov chains, their asymptotic completeness and ergodic theory, with applications to quantum optics. Their focal point is shifting towards quantum information and control theory, an area which is rapidly becoming relevant to experimental physicists.

Ross Kang conducts research in probabilistic and extremal combinatorics, with emphasis on graphs (which abstractly represent networks). He works in random graph theory (the study of stochastic models of networks) and often uses the probabilistic method. This involves applying probabilistic tools to shed light on extremes of large-scale behaviour in graphs and other combinatorial structures. He has focused a lot on graph colouring, an old and popular subject made famous by the Four Colour Theorem (erstwhile Conjecture).

See the website http://www.ru.nl/masters/mathematics/stochastics

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The MSc in Risk and Stochastics offers in-depth instruction in advanced mathematical risk theory and its ramifications in finance, insurance, and risk management. Read more

About the MSc programme

The MSc in Risk and Stochastics offers in-depth instruction in advanced mathematical risk theory and its ramifications in finance, insurance, and risk management. It draws on world-class research in modern financial and actuarial mathematics within the Department. The programme is LSE’s timely response to the strong developments in the interface of finance and insurance, which is manifest in mergers across the industries.

It will provide you with instruction in theoretical as well as practical aspects of various techniques in risk management. It draws on diverse quantitative disciplines from mathematical finance and actuarial science to statistics. Students work with real financial data to receive hands-on training in real-world problems. You can expect high-level training in quantitative methods with applications in the management of financial and insurance risk and the interplay between finance and insurance sectors.

The programme aims to prepare candidates for a range of expert careers in financial and insurance industries, in regulatory bodies, and in applied and theoretical research.

Graduate destinations

The programme offers excellent prospects for employment and further study. Students can gain employment in the finance or insurance industries. They can also go on to do a higher degree. The Department has good relations with the financial services industry, particularly insurance and professional bodies.

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The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate. Read more

Mathematics in Nijmegen: From Applied Stochastics to Infinity-Categories

The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate. Its wide scope, which ranges from medical statistics to the mathematical foundations of computer science, physics and even mathematics itself, reflects the diversity of research at the Institute for Mathematics, Astrophysics and Particle Physics (IMAPP).
Mathematical research of course stands on its own, as is notably the case with the large group in algebraic topology led by Spinoza laureate Ieke Moerdijk. In addition, within IMAPP, researchers link with high-energy physics, including Higgs physics and quantum gravity. Outside IMAPP but within the Faculty of Science, there are close ties with the Institute for Computing and Information Sciences (ICIS) (think of logic and category theory) and outside the Faculty of Science (but within Radboud University) researchers at both the Donders Institute for Neurosciences and the University Medical Center collaborate with the applied stochastics group.

See the website http://www.ru.nl/masters/mathematics

Specialisations within the Master's Programme in Mathematics

- Algebra & Topology
- Applied Stochastics
- Mathematical Physics
- Mathematical Foundations of Computer Science

Quality label

For the fourth time in a row, this programme was rated number one in the Netherlands in the Keuzegids Masters 2015 (Guide to Master's programmes).

Career prospects

Mathematicians are needed in all industries, including the industrial, banking, technology and service industry and also within management, consultancy and education. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad indeed and is why many graduates of a Master’s in Mathematics find work very quickly.

Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

- PhD positions
Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.

See the website http://www.ru.nl/masters/mathematics

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* Ranked within the UK top 10 Business Schools according to The Times and The Sunday Times Good University Guide 2015 and The Complete University Guide 2016. Read more
* Ranked within the UK top 10 Business Schools according to The Times and The Sunday Times Good University Guide 2015 and The Complete University Guide 2016

* EQUIS accredited placing us in the top 1% of business schools globally

* Connections with an extensive and diverse range of businesses including Canon, Thomson Reuters, Lloyds Banking Group, IBM, Coca Cola and the Met Office

* Our teaching is research-led – you will study with internationally respected academics who are experts in their fields
We have partnerships with over 40 overseas universities or business schools and this figure is growing all the time

Quantitative financial methods are one of the fastest growing areas of the present day banking and corporate environments. The solution by Black, Scholes and Merton of the option pricing problem set off a revolution in finance resulting in the introduction of sophisticated mathematical techniques in the financial markets and corporate planning.

To understand, apply and develop these sophisticated methods requires a good understanding of both advanced mathematics and advanced financial theory. By combining the financial expertise in the University of Exeter Business School with expertise in the Mathematical Research Institute of the Mathematics Department at the University, this intensive MSc programme will prepare you for careers in areas such as international banking or international business. For those with a strong mathematical background, and a wish to pursue a finance career, this programme is the ideal introduction to this exciting field.

Careers

The programme prepares you for a career in financial modelling within financial institutions themselves and within other sectors. It builds upon the success of Exeter’s well-established range of Masters programmes in Finance and related areas, many of whose graduates now hold senior positions in areas such as corporate financial strategy, financial planning, treasury and risk management and international portfolio management.
With the strong links between the College and the Met Office, the course also prepares you for career opportunities within reinsurance and credit risk management, especially in the development of financial models that rely on weather/climate systems.

Programme structure

The taught element of the programme takes place between October and May and is arranged into two 12-week teaching semesters. The modules we outline here provide examples of what you can expect to learn on this degree course based on recent academic teaching. The precise modules available to you in future years may vary depending on staff availability and research interests, new topics of study, timetabling and student demand.

Compulsory modules

Recent examples of compulsory modules are as follows; Methods for Stochastics and Finance; Analysis and Computation for Finance; Mathematical Theory of Option Pricing; Fundamentals of Financial Management; Research Methodology and Advanced Mathematics Project.

Optional modules

Some recent examples are as follows; Topics in Financial Economics; Investment Analysis; Banking and Financial Services; Derivatives Pricing; Domestic and International Portfolio Management; Financial Modelling; Advanced Corporate Finance; Alternative Investments; Quantitative and Research Techniques; Advanced Econometrics; Dynamical Systems and Chaos; Pattern Recognition; Introduction to C++ and Level 3 Mathematics Modules

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The MSc Applicable Mathematics is an innovative programme, drawing together traditional and modern mathematical techniques in a variety of social science contexts. Read more

About the MSc programme

The MSc Applicable Mathematics is an innovative programme, drawing together traditional and modern mathematical techniques in a variety of social science contexts. It is designed both for mathematicians who wish to make themselves more marketable by adding some social science aspects to their knowledge and skills base, and for non-mathematicians with strong quantitative backgrounds who wish to add to and improve their understanding of the mathematics behind much of social science.

The programme will provide you with an increased knowledge of mathematics, particularly in algorithms, game theory, discrete mathematics, probability and stochastics, and optimisation, in addition to training in appropriate computational methods. Reflecting the world's dependence on computation, students will learn the programming language Java, and how to use it to apply their knowledge to real-world problems.

The skills and knowledge gained over the programme will open up a wide range of potential careers, including finance, business, software development, and industry. It will also provide a solid base for further studies at research level.

Graduate destinations

This programme is ideal preparation for a range of careers in industry, finance, government and research. Graduates of the programme have found employment in companies such as Amazon; BlackRock; Credit Suisse; Facebook; Goldman Sachs; Google; KPMG; National Grid and RBS.

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Quantitative financial methods are one of the fastest growing areas of the present day banking and corporate environments. Read more
Quantitative financial methods are one of the fastest growing areas of the present day banking and corporate environments. The solution by Black, Scholes and Merton of the option pricing problem set off a revolution in finance resulting in the introduction of sophisticated mathematical techniques in the financial markets and corporate planning.

To understand, apply and develop these sophisticated methods requires a good understanding of both advanced mathematics and advanced financial theory. By combining the financial expertise in the University of Exeter Business School with expertise in the Mathematical Research Institute of the Mathematics Department at the University, this intensive MSc programme, available over 9 or 12 months, will prepare you for careers in areas such as international banking or international business. For those with a strong mathematical background, and a wish to pursue a finance career, this programme is the ideal introduction to this exciting field.

Programme structure

The taught element of the programme takes place between October and May and is arranged into two 12-week teaching semesters.

Compulsory modules

The compulsory modules can include; Methods for Stochastics and Finance; Analysis and Computation for Finance; Mathematical Theory of Option Pricing; Fundamentals of Financial Management; Research Methodology and Advanced Mathematics Project;

Optional modules

Some examples of the optional modules are as follows; Topics in Financial Economics; Investment Analysis; Banking and Financial Services; Derivatives Pricing; Domestic and International Portfolio Management; Investment Analysis; Financial Modelling; Advanced Corporate Finance; Alternative Investments; Quantitative and Research Techniques; Advanced Econometrics; Dynamical Systems and Chaos; Pattern Recognition; Introduction to C++ and Level 3 Mathematics Modules.

The modules we outline here provide examples of what you can expect to learn on this degree course based on recent academic teaching. The precise modules available to you in future years may vary depending on staff availability and research interests, new topics of study, timetabling and student demand.

Learning and teaching

Teaching is by lectures, example classes, computer classes, tutorials, set work, project work, reading and self-study. The exact form and number of the lectures and tutorials varies from module to module and is chosen according to the material to be covered.
You will use the computer programming language Matlab and online financial databases such as Bloomberg and Datastream.

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Mathematics is a core scientific subject and an essential basis for a range of other sciences. Read more
Mathematics is a core scientific subject and an essential basis for a range of other sciences. This programme brings together the latest developments in a range of mathematical disciplines to provide you with a thorough grounding in the subject, together with a substantial project that can be used to develop a specialisation.

Internationally leading research supports this programme, with particular research strengths including magnetic fields, interface of algebraic number theory and abstract algebra, climate system dynamics and display-structure on crystalline cohomology.
The programme prepares you for a career in numerous industries or for progression to a PhD for those interested in pursuing a research pathway.

Programme structure

The programme comprises three compulsory taught modules and 90 credits of option modules. The taught component of the programme is completed in June with the project extending over the summer period for submission in September.

Compulsory Modules

The compulsory modules can include; Research in Mathematical Sciences; Advanced Mathematics Project and Analysis and Computation for Finance

Optional Modules

Some examples of the optional modules are as follows;
Logic and Philosophy of Mathematics; Methods for Stochastics and Finance; Mathematical Theory of Option Pricing; Dynamical Systems and Chaos; Fluid Dynamics of Atmospheres and Oceans; Modelling the Weather and Climate; The Climate System; Algebraic Number Theory; Algebraic Curves; Waves, Instabilities and Turbulence; Magnetic Fields and Fluid Flows; Statistical Modelling in Space and Time and Mathematical Modelling in Biology and Medicine.

The modules we outline here provide examples of what you can expect to learn on this degree course based on recent academic teaching. The precise modules available to you in future years may vary depending on staff availability and research interests, new topics of study, timetabling and student demand.

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This programme is for students with an undergraduate degree containing a significant component of Mathematics who wish to upgrade their degree in Mathematics and spend a year in a leading UK Mathematics Department. Read more
This programme is for students with an undergraduate degree containing a significant component of Mathematics who wish to upgrade their degree in Mathematics and spend a year in a leading UK Mathematics Department. On completion with a Merit or Distinction you may be considered for the MSc programme.

Key benefits

- An intensive programme preparing students for further study at MSc and PhD level and for work in the non-academic sector.

- A flexible programme allowing students to plan an individual programme.

- A transitional programme providing students with an excellent opportunity to upgrade their degree in Mathematics.

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/mathematics-grad-dip.aspx

Course detail

- Description -

You will attend eight of the courses currently offered to BSc or MSci students. Subject to timetable constraints, considerable choice is possible. The courses available, which change slightly from year to year, include.

- Course purpose -

For students with an undergraduate degree or equivalent who wish to have the experience of one year in a leading UK Mathematics Department, or who may not be immediately eligible for entry to a higher degree in the UK and who wish to upgrade their degree. If you successfully complete this programme with a merit or distinction we may consider you for the MSc programme.

- Course format and assessment -

You must take eight modules which may include an individual project on a subject of your choice. Examples of modules are listed below:

- Elementary Number Theory
- Partial Differential Equations & Complex Variables
- Linear Algebra
- Geometry of Surfaces
- Real Analysis II
- Complex Analysis
- Galois Theory
- Topology
- Special Relativity & Electromagnetism
- Introductory Quantum Theory
- Space-time Geometry & General Relativity
- Mathematical Finance I: Discrete Time
- Mathematical Finance II: Continuous Time
- Rings & Modules
- Representation Theory of Finite Groups
- Control Theory
- Stochastics
- Fourier Analysis
- Applied Analytic Methods
- Project (mathematical topic)

You will also take examinations, mostly in May/June.

Career prospects

Further study at MSc and PhD level, employment as analysts in investment banks and industrial researchers in large companies.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx

About Postgraduate Study at King’s College London:

To study for a postgraduate degree at King’s College London is to study at the city’s most central university and at one of the top 20 universities worldwide (2015/16 QS World Rankings). Graduates will benefit from close connections with the UK’s professional, political, legal, commercial, scientific and cultural life, while the excellent reputation of our MA and MRes programmes ensures our postgraduate alumni are highly sought after by some of the world’s most prestigious employers. We provide graduates with skills that are highly valued in business, government, academia and the professions.

Scholarships & Funding:

All current PGT offer-holders and new PGT applicants are welcome to apply for the scholarships. For more information and to learn how to apply visit: http://www.kcl.ac.uk/study/pg/funding/sources

Free language tuition with the Modern Language Centre:

If you are studying for any postgraduate taught degree at King’s you can take a module from a choice of over 25 languages without any additional cost. Visit: http://www.kcl.ac.uk/mlc

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Programme structure. The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. Read more
Programme structure
The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. There are examinations and coursework in eight modules altogether, including the four core modules. Additionally, all students complete a dissertation.

Core modules
0.Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.


0.Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.


0.Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.


0.Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.

Elective modules

0.Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.


0.Information in finance with application to credit risk management. An innovative and intuitive approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing – a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.

0.Mathematical theory of dynamic asset pricing. Financial modelling and risk management involve not only the valuation and hedging of various assets and their positions, but also the problem of asset allocation. The traditional approach of risk-neutral valuation treats the problem of valuation and hedging, but is limited when it comes to understanding asset returns and the behaviour of asset prices in the real-world 'physical' probability measure. The pricing kernel approach, however, treats these different aspects of financial modelling in a unified and coherent manner. This module introduces in detail the techniques of pricing kernel methodologies, and its applications to interest-rete modelling, foreign exchange market, and inflation-linked products. Another application concerns the modelling of financial markets where prices admit jumps. In this case, the relation between risk, risk aversion, and return is obscured in traditional approaches, but is made clear in the pricing kernel method. The module also covers the introduction to the theory of Lévy processes for jumps and its applications to dynamic asset pricing in the modern setting.

0.Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Risk measures, preference and portfolio choice. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic to work on, which will lead to the preparation of an MSc dissertation. This can be thought of as a mini research project. The project supervisor will usually be a member of the financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

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This exciting new programme introduces modern mathematical techniques and financial modelling, such as portfolios options and derivative pricing, for students with a mathematical background. Read more
This exciting new programme introduces modern mathematical techniques and financial modelling, such as portfolios options and derivative pricing, for students with a mathematical background. In particular it will introduce the probability and stochastics often not included in standard mathematics degrees.

Following the Financial Crisis of 2007-2009 there has been a shift in the practice of mathematical finance. The emphasis is now on possessing a broad range of skills that can be applied to practical problems. The aim is to understand, both quantitatively and qualitatively, risks and uncertainty involved.

The MSc focuses on practical computational and applied mathematics aspects of finance and uncertainty, and students graduating from the programme will have excellent employment prospects that are not restricted to any one narrow sector of financial services.

We have a practical applied approach to the material. This will provide you with relevant and modern skills, in demand in the UK and internationally, relating to structured finance.

Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:

Core Courses

Modelling and Tools;
Derivative Markets, Pricing and Financial Modelling;
Statistical Methods (recommended);
Stochastic Simulation;
Modern Portfolio Theory.

Optional Courses

Optimization;
Enterprise Risk Management;
Data mining and Machine Learning;
Financial Markets;
Software Engineering Foundations;
Bayesian Inference and Computational Methods;
Financial Engineering;
Numerical Analysis (PDEs);
Advanced Derivative Pricing;
Numerical Techniques for PDE's with either Time Series or Financial Econometrics;
Advanced Software Engineering.

Progression to the MSc project phase is dependent on assessed performance.

Typical project topics may include

Applications of multilevel Monte-Carlo sampling in finance;
An investigation of new numerical methods for stochastic interest rate models;
Space time adaptivity for Fokker—Planck equations.

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The MSc Computational Finance will provide you with mathematical and computational skills required to solve real problems in quantitative finance. Read more
The MSc Computational Finance will provide you with mathematical and computational skills required to solve real problems in quantitative finance. Many areas of modern finance such as risk management and option pricing emphasise numerical and computational skills as well as an understanding of the mathematical background.

The programme brings together expertise from Mathematics and the Business School to ensure a balanced approach to many of the complex problems in modern quantitative finance.

On completion of the programme you will be able to review and implement complex financial models in a number of programming languages including C++, MATLAB and R.

Programme structure

Core modules

The compulsory modules can include; Methods for Stochastics and Finance; Analysis and Computation for Finance; Mathematical Theory of Optional Pricing; Introduction to C++; Computational Finance with C++; Numerical Finance; Research Methodology; Advanced Mathematics Project; Investment Analysis I; Investment Analysis II; Financial Modeling

Optional modules

Some examples of the optional modules are as follows; Topics in Financial Economics; Banking and Financial Services; Derivatives Pricing; Domestic and International Portfolio Management; Advanced Corporate Finance; Alternative Investments; Quantitative Research Techniques; Advanced Econometrics;

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Computer Science is one of the drivers of technological progress in all economic and social spheres. Those graduating with an M.Sc. Read more

About Computer Science

Computer Science is one of the drivers of technological progress in all economic and social spheres. Those graduating with an M.Sc. in Computer Science are specialists in at least one field of computer science who have wide-ranging science-based methodological expertise.
Graduates are able to define, autonomously and comprehensively, computer science problems and their applications, structure them and build abstract models. Moreover, they are able to define and implement solutions that are at the state of the art of technology and science.

Features

– A broad, international and relevant selection of courses
– As a student, you will work on cutting-edge research projects
– Individual guidance in small learning groups
– Excellent enterprise relations maintained by the chairs and institutes
– Numerous partnerships with universities throughout the world, including a double degree programme with the Institut national des sciences appliquées de Lyon (INSA)

Syllabus

The programme offers the following five focus modules:
1) Algorithms and Mathematical Modelling
2) Programming and Software Systems
3) Information and Communication Systems
4) Intelligent Technical Systems
5) IT Security and Reliability
1) Algorithms and Mathematical Modelling: This module teaches you about determinstic and stochastic algorithms, their implementation, evaluation and optimisation. You will acquire advanced knowledge of computer-based mathematical methods – particularly in the areas of algorithmic algebra and computational stochastics – as well as developing an in-depth expertise in mathematical modelling and complexity analysis of discrete and continuous problems.
2) Programming and Software Systems: This module imparts modern methods for constructing large-scale software systems, as well as creating and using software authoring, analysis and optimisation tools. In this module you will consolidate your knowledge of the various programming paradigms and languages, the structure of language processing systems, and learn to deal with parallelism in program procedures.
3) Information and Communication Systems: In this module you will study the interactions of the classic computer science areas of information systems and computer networks. This focus area represents an answer to the problem of increasing volume and complexity of worldwide information distribution and networks, and for the growing requirements on quality and performance of computer communication. Additionally, you will learn to transfer database results to multimedia data.
4) Intelligent Technical Systems: In this module you are acquainted with digital image and signal processing, embedded systems and applications of intelligent technical systems in industrial and assistance systems, which are necessary for production automation and process control, traffic control, medical and building technology. You will learn to develop complex applications using computer systems and deal with topics such as image reconstruction, camera calibration, sensor data fusion and optical measurement technology.
5) IT Security and Reliability: This module group is concerned with security and reliability of IT systems, e.g. in hardware circuitry and communication protocols, as well as complex, networked application systems. To ensure the secure operation of these systems you will learn design methodology, secure architectures and technical implementation of the underlying components.

Language requirements

Unless English is your native language or the language of your secondary or undergraduate education, you should provide an English language certificate at level B2 CEFR, e.g. TOEFL with a minimum score of 567 PBT, 87 iBT or ITP 543 (silver); IELTS starting from 5.5; or an equivalent language certificate.

To facilitate daily life in Germany, it would be beneficial for you to have German language skills at level A1 CEFR (beginner’s level). If you do not have any German skills when starting out on the programme, you will complete a compulsory beginner’s German course during your first year of study.

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Working at a frontier of mathematics that intersects with cutting edge research in physics. Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. Read more
Working at a frontier of mathematics that intersects with cutting edge research in physics.

Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.

Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.

At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.

See the website http://www.ru.nl/masters/mathematics/physics

Why study Mathematical Physics at Radboud University?

- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.
- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.
- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.
- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.

Career prospects

Mathematicians are needed in all industries, including the industrial, banking, technology and service industry and also within management, consultancy and education. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad indeed and is why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

PhD positions

Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.

Our research in this field

The research of members of the Mathematical Physics Department, emphasise operator algebras and noncommutative geometry, Lie theory and representation theory, integrable systems, and quantum field theory. Below, a small sample of the research our members pursue.

Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.

Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:
1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.
2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

See the website http://www.ru.nl/masters/mathematics/physics

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Programme structure. The programme offers five "core" modules, taken by all candidates, along with a variety of elective modules from which students can pick and choose. Read more
Programme structure

The programme offers five "core" modules, taken by all candidates, along with a variety of elective modules from which students can pick and choose. There are lectures, examinations and coursework in eight modules altogether, including the five core modules. Additionally, all students complete an individual research project on a selected topic in financial mathematics, leading to the submission of a dissertation.

Core modules

Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.

Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.

Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.


Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.

Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.

Elective modules

Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.

Information in finance with application to credit risk management. An innovative and intuitive approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing – a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.


Mathematical theory of dynamic asset pricing. Financial modelling and risk management involve not only the valuation and hedging of various assets and their positions, but also the problem of asset allocation. The traditional approach of risk-neutral valuation treats the problem of valuation and hedging, but is limited when it comes to understanding asset returns and the behaviour of asset prices in the real-world 'physical' probability measure. The pricing kernel approach, however, treats these different aspects of financial modelling in a unified and coherent manner. This module introduces in detail the techniques of pricing kernel methodologies, and its applications to interest-rete modelling, foreign exchange market, and inflation-linked products. Another application concerns the modelling of financial markets where prices admit jumps. In this case, the relation between risk, risk aversion, and return is obscured in traditional approaches, but is made clear in the pricing kernel method. The module also covers the introduction to the theory of Lévy processes for jumps and its applications to dynamic asset pricing in the modern setting.


Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.

Risk measures, preference and portfolio choice. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic for an individual research project, which will lead to the preparation and submission of an MSc dissertation. The project supervisor will usually be a member of the Brunel financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

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This course is designed for graduates of quantitative disciplines who want to kick-start a career in actuary. It provides a solid foundation in statistics, financial mathematics, economics and business finance. Read more
This course is designed for graduates of quantitative disciplines who want to kick-start a career in actuary. It provides a solid foundation in statistics, financial mathematics, economics and business finance. Upon completion of the course, your knowledge and skills could be applied to a range of industries in the financial services such as insurance, pensions, healthcare, banking, investment and risk assessment.

You will be equipped with mathematical and statistical knowledge and problem-solving skills to help businesses and institutions evaluate the long-term financial implications of the decisions they make. You will also have the opportunity to undertake a minor dissertation involving the study of a number of problems specific to the insurance and financial sector.

The Institute and Faculty of Actuaries has approved programme-level exemption status for the MSc programme in Actuarial Science at UCC in respect of their first 8 Core Technical subjects. Students may be recommended for exemption from the Institute’s own professional examinations in up to 7 of these Core Technical subjects by performing sufficiently well in the corresponding examinations of the MSc programme. UCC is one of the very few universities in Ireland which can offer students the potential to receive this level of exemptions from the professional actuarial examinations.

Visit the website: http://www.ucc.ie/en/ckr46/

Course detail

This is exciting course allows you to kick-start your career in actuary. It has similar core technical coverage to UCC’s very successful undergraduate course, which, over the last number of years, has achieved close to 100% employment. Graduates of this course are expected to also have no difficulty in gaining employment.

Format

The teaching methods used will be a combination of lectures, tutorials, computer practicals and directed study. You can expect to have approximately 22 hours per week of lectures, tutorials and directed study in semesters 1 and 2 and about 10 hours per week of directed study in semester 3.

Part 1

- Core modules (50 credits) -

PA6007 Market Analysis Methods for Actuarial Science (10 credits)
ST6001 Theory of Annuities - Certain for Actuarial Science (10 credits)
ST6002 Applied Financial Reporting Methods for Actuarial Science (10 credits)
ST6003 Probability & Mathematical Statistics for Actuarial Science (10 credits)
ST6004 Mortality Studies and Life Table Analysis for Actuarial Science (10 credits)

- Elective Modules (10 credits) -

ST6006 Insurance Risk Modelling for Actuarial Science (10 credits)
or
ST6010 Current Topics in Statistical Applications to Actuarial Science (10 credits).

*Were a student to enter the programme with sufficient background knowledge, as determined by the programme co-ordinator, in one of the above core modules, then that student would take both electives specified.

Part II

- Core module (20 credits) -

ST6009 Application of Core Technical Research Methodologies in Actuarial Science (20 credits)

- Elective modules (10 credits) -

ST6005 Life Contingencies for Actuarial Science (10 credits)
or
ST6008 Applied Financial Modelling and Risk Stochastics for Actuarial Science (10 credits)

Part-time students take modules ST6001, ST6003 and PA6007 in Year 1 and the remaining modules, including electives where appropriate, in Year 2.

Assessment

All taught modules in this course are assessed via a combination of end-of-module examination and submission of a portfolio of research and directed study.

For actuarial exemption purposes, the appointed actuarial independent examiner will base their recommendations for an exemption in the corresponding CT subject, on a student's performance in the final examination

For the research module (ST6009), you will study a number of problems, specific to the insurance and financial sector, and use the methodologies developed in the earlier modules to analyse such problems and produce oral and written reports on your work.

Careers

An actuarial qualification gives an excellent grounding in subjects like economics, finance, mathematics, and statistics, as well as the more actuarial subjects. This makes actuarial graduates suitable for a range of careers, not just actuarial work.

How to apply: http://www.ucc.ie/en/study/postgrad/how/

Funding and Scholarships

Information regarding funding and available scholarships can be found here: https://www.ucc.ie/en/cblgradschool/current/fundingandfinance/fundingscholarships/

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