Stochastic optimization in mathematical finance

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The problem of making decisions while facing an uncertain future pervades all aspects of human activity. This fundamental problem is perhaps most evident in the fields of finance and insurance. Insurance allows individuals to reduce the impact of the risks they face by pooling them together and sharing the consequences. Investors employ financial markets both to hedge their risks, and to speculate on the risks they wish to assume. The proposed research program will develop and apply the techniques of stochastic optimization to problems in finance and insurance. Special emphasis is placed on problems arising from recent developments in financial markets, including the rapid growth of the market for credit risk and credit derivatives, the prevalence of hedge funds and the need to measure and manage their performance, and developments in insurance including the introduction of new products with embedded options and the changing regulatory environment.