Professor William T Shaw, MA, DPhil, FIMA

Mathematics and Computation of Risk

Room 809
Tel:- 020-7679-2858
E-mail:- w.shawucl.ac.uk
Fax: 020-7383-5519

Research Interests
Financial Mathematics, Quantile Theory, Monte Carlo Methods, Risk Optimization, Computer Algebra, Financial Computing

I am interested in a broad class of problems sitting at the interfaces between classical applied mathematics, statistics and computation, with a common motivation from financial problems associated with risk and derivatives. A unifying thread is the use of non-Gaussian models in finance. I investigate the computation and minimization of risk within such models, and also seek fundamental explanations of non-Gaussian behaviour in terms of market microstructure.

One current theme is the characterization of quantile functions (inverse cumulative distribution functions) by non-linear ordinary and partial differential equations. The use of ODEs and PDEs gives much greater flexibility in the development of quantiles for fast Monte Carlo applications, as well as allowing their treatment by classical methods. The optimization of quantiles for modern parallel computing environments (GPUs) is under study.

The topic of risk minimization is under study from a parallel computation viewpoint. We wish to minimize quite general risk functions (VaR, CVaR, Utility,...) for portfolios without restrictions as to the asset return distributions. The origins of non-Gaussian behaviour is also under investigation. One project looks at the use of hybrid Brownian motions capable of producing a diverse collection of asset return distributions (Student t, gamma, Johnson-SU), and their motivation from technical trading. Another study explores the use of stochastic volatility models.

Other projects look more generally at the perception of risk and its sensitivities to choices of risk measure, dependency structure, marginal distributions and event frequency. I am also interested in applications to broader areas of applied mathematics of complex variable theory and computer algebra.