PhD Seminar Series in Advanced Mathematical Methods in Economics & Finance

This page archives video and handouts from the first PhD Seminar Series on Advanced Mathematical Methods in Economics & Finance hosted by the School of Economics & Finance of the University of St Andrews.

The Seminar Series serves as a vehicle to provide additional training to young researchers willing to develop their mathematical skills at an advanced level and to apply them in various fields. International scholars present a portfolio of techniques including general fixed point theorems, Brownian motions, optimal control, stochastic calculus, evolutionary dynamics and cooperative game theory. Young researchers have the opportunity to present and discuss their own research, exchange ideas, interact with the guest lecturer and participate in discussions.

The Seminar Series was sponsored by the Economics Network. The organisers gratefully acknowledge the help of GRADSkills (University of St Andrews) and the Scottish Graduate Programme in Economics.

Lectures

What Mathematics does a Quant need to know? (Friday 7 November)

The Inaugural Lecture, delivered by Dr Robert Campbell, covers 1) the purpose of an investment bank, 2) applications of mathematics to the pricing and trading of derivatives and 3) the daily life and career progression of a "quant" in an investment bank.

Dr Campbell is a partner in Ravenscourt Capital, a London based hedge fund that specialises in the trading of distressed debt and derivatives. He has over twenty years of experience of working at senior levels in investment banking. He was a Managing Director and Head of Quantitative Research at Lehman Brothers where he worked for twelve years and before that he worked for six years at Salomon Brothers. He is also an honorary Professor of Applied Mathematics at St Andrews University where he obtained his PhD.

How to invest optimally in a market? (Friday 28 November)

Professor Ralf Korn speaks about modern portfolio optimization techniques and how real traders apply them. He includes topics such as Defaultables and Market Crash hedging, which in current times of credit crunch and sub prime crisis are extremely relevant. The mathematical techniques used for that sort of modelling are explained in detail.

Prof Korn is Dean of Mathematical Sciences at the University of Kaiserslautern (Germany). His main areas of research are in financial mathematics (portfolio optimization, transaction costs, modelling of inflation, dividends and longevity) and stochastic control (control of continuous-time stochastic processes with applications in finance, worst-case-control). He is the Associate Editor of "Mathematical Methods of Operations Research" and the Associate Editor of "Mathematical Finance".

Aspects on Brownian Motions and Applications in Asian Options (Wednesday 10 December)

Professor Marc Yor speaks about his contributions to the theory of Asian options and Brownian functionals. Asian options are the most frequently traded OTC derivatives, and are becoming more and more popular. Prof Yor was the first to systematically study these options, and his Laplace inversion method is used frequently by financial institutions to price and hedge Asian options.

Marc Yor is Professor at the Université de Paris 6 - Pierre et Marie Curie (France). He belongs to the Probabilities and Random Models Laboratory and leads the research team on Brownian Motion and Stochastic Calculus.

Stochastic Agent-Based Models in Economics and Finance (Thursday 8 January)

Professor Thomas Lux speaks on how economic systems can be seen as evolutionary models, where agents interact with each other and a selection process favours the most successful. He introduces underlying dynamical systems as well as the necessary game theoretic concepts.

Thomas Lux is Professor of Monetary Economics and International Finance at the University of Kiel (Germany) and Research Associate at the Kiel Institute for the World Economy. He is the Member of Editorial Board of several journals including "Quantitative Finance", "Journal of Economic Behavior and Organization" and the "Journal of Economic Interaction and Cooperation". His research concentrates on theoretical and empirical aspect of financial markets and monetary economics. The major focus of this research has been on behavioural, agent-based models of financial markets.

Dynamical Systems (Thursday 26 February)

Dr Pierre Cartigny speaks about dynamical systems, stability, optimal control and differential games and their applications in Economics and Biology, in resource extraction in particular.

Dr Cartigny is Director of the Joint Research Unit for Systems Analysis and Biometrics at INRA in Montpellier (France). He is Associate Professor at the Université de la Mediterranée (France) and Research Associate at GREQAM in Marseille (France). His research interests mainly focus on modelling, analysing and controlling dynamic systems of biological, agronomical or environmental interest. These systems rely on the theory of complex system defined by ordinary or partial differential equations and on optimal theory.

Value at risk and self-similarity (Tuesday 17 March)

Dr Olaf Menkens speaks about Value at Risk and Self-similarity, the distribution of stock prices and returns. He has analyzed empirical data and will in particular discuss the issue how to estimate the so called Hurst parameter which models a memory effect on stock prices.

Dr Menkens is Lecturer in the School of Mathematical Sciences at Dublin City University (Ireland). His research interests are in mathematical finance, in particular crash hedging strategies and optimal portfolios under the threat of a crash, value at risk and self-similarity, insider trading and liquidity risk.

Unit Root Distribution Theory (Thursday 23 April)

Professor Rod McCrorie's first lecture discusses the underpinnings of unit root distribution theory, especially from the point of view of functional central limit theory. The second lecture considers how to derive and compute the densities of relevant test statistics, using the stochastic process approach, the Fredholm approach and the Imhof method. An attempt will be made to relate this material to the wider probability literature.

Rod McCrorie is Professor in the School of Economics and Finance at the University of St Andrews. His research interests are Econometric Theory, Applied Macroeconomics and Time Series Analysis.

Stochastic Differential Equations (Wednesday 13 May, Rescheduled from 5 February)

Dr Evelyn Buckwar speaks about stochastic differential equations. Starting from ordinary differential equations, she discusses Brownian motion and how it can be used to include the aspect of uncertainty in a continuous time dynamic framework. She emphasizes the point on how one deals with stochastic differential equations numerically, how to simulate paths, how to use them to compute the price of an option via Monte Carlo simulation for example, but also discuss applications in Economics, such as the stochastic Solow model and from Biology, in particular Population dynamics.

Dr Buckwar is Lecturer in the Department of Mathematics at Heriot-Watt University (UK). Her research interests focus on the analysis and numerical analysis of stochastic differential equations with and without memory terms, as well as applications in neuroscience, population dynamics and finance.

Fractional Brownian motion and applications (Monday 25 May)

The fractional Brownian motion (fBm) is an extension of the classical Brownian motion that allows its disjoint increments to be correlated. In the last decade, and motivated by empirical results, several authors have studied models driven by the fBm. This seminar will be devoted to introduce the basic concepts and techniques regarding fBm, as well as to discuss some of its applications in finance (how it can be used to describe the long and the short-time behaviour of the implied volatility) and physics (its connection with fractal analysis in surface growth modeling).

Dr Elisa Alos is Associate Professor in the Faculty of Economics at the University Pompeu Fabra (Spain). Her research interests lie in stochastic calculus, stochastic partial differential equations and mathematical finance.

Further information:

Dr Laurence Lasselle
E-mail: LL5@st-andrews.ac.uk
Tel: 01334 462 451
Fax: 01334 462 444

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