The project "Mathematical Methods in Financial Risk Management" focuses on methodological problems in the modeling of risks. Members of the project research group examine issues arising in the presence of market imperfections as well as statistical issues.
Market imperfections include a lack of liquidity, transaction costs, jumps in the price process, etc. They typically preclude market participants from perfectly hedging derivatives. New criteria to value and handle the unhedgeable risk need to be developed. Researchers in this project develop pricing bounds and optimal hedging strategies that take such market imperfections into account.
Market imperfections also present formidable challenges to measuring risks. A new type of risk models, known as "coherent risk measures", were developed by members of this project and have become widely known. These measures are now being extended from the single period case to the multi-period case, and from fixed positions to dynamic portfolios.
The group also addresses statistical issues arising in risk management and pricing of derivatives. Extreme value theory, championed by members of this group, is being extended to model dependence in multivariate time series and to allow for higher dimensional distributions. Furthermore, dependence modeling is being included in derivatives pricing models.
The "Mathematical Methods in Financial Risk Management" group mainly comprises mathematicians specialized in probability theory and stochastic processes as well as statistical aspects.