Research project In this research program we intend to substantially refine several of the main mathematical tools used in modern risk management, make mathematical progress within a number of key problem areas, several which include partial differential equations, as well as to apply these results to relevant industrial problems.
The rapid development of the financial sector, its complexity and the exponential growth of exotic products have made mathematics an indispensible tool within large banks and financial institutions in general. Commercial banks, insurance and reinsurance companies, asset management funds, hedge funds, pension funds and major electric power companies all try to develop models for the pricing of exotic products, for risk management as well as in order to be able to optimize the return on their portfolios given restrictions on risk measures. On a very general level the mathematical toolbox of modern mathematical finance and risk management is to large extent concentrated to multidimensional stochastic processes in continuous and discrete time as well as multivariate distributions in general, partial differential equations, harmonic analysis and optimization. The purpose of the project is to refine several of the main mathematical tools used in modern risk management