Mixed methods in computational finance

The evaluation of functionals of stochastic processes is one of the key problems in the new branch of applied mathematics that is known as computational finance. The problem, and related questions such as differentiation with respect to parameters of underlying process, can be formulated in stochastic terms or in terms of partial differential equations. Accoringly, various numerical methods (such as Monte carlo, Quasi Monte Carlo and finite differences) have been applied and have been shown to lead to satisfactory results under suitable conditions. However, there is a strong tendency in the application field to consider highly complex problems which cannot be easily treted by any single method. For some of these problems, promising results have already been obtained with "mixed" methods that combine several techniques. The research proposed here is concerned with a systematic investigation of the ways in which techniques from different domains can be made to cooperate to solve difficult computational problems in financial mathematics.