Stochastic optimization in mathematical finance

在面对不确定的未来的同时做出决定的问题贯穿于人类活动的方方面面。这个根本问题可能在金融和保险领域最为明显。保险使个人能够通过将他们面临的风险汇集在一起并分担后果来减少他们面临的风险的影响。投资者利用金融市场来对冲他们的风险，并对他们希望承担的风险进行投机。拟议的研究计划将开发和应用随机优化技术来解决金融和保险领域的问题。特别强调了金融市场最近的发展所产生的问题，包括信用风险和信用衍生工具市场的迅速增长、对冲基金的盛行以及衡量和管理其业绩的必要性，以及保险业的发展，包括推出具有嵌入期权的新产品和不断变化的监管环境。

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.