Partial Differential Equations and Financial Risk Management on an Industrial Scale
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 purpose of the project is to refine several of the main mathematical tools used in modern risk management
Participating departments and units at Umeå University
The rapid development of the financial sector, its complexity and the exponential growth of exotic products have made mathematics an indispensable 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.
This research program is built on a number of subprojects and each such subproject focuses on a well defined problem arising in mathematical finance and/or partial differential equations. A theme of the project is to use and develop methods and techniques for multidimensional problems which also can be used in industrial applications. In the following we list the titles of some of the subprojects described in our research program.
•A framework for non-maturing liabilities •A framework for the pricing of structured finance products •Free boundary problems and the pricing of options of American type •Analysis of systems of stochastic partial differential equations