Development of the methods of stochastic control and filtering in mathematical finance

我们将涉及期望效用最大化和衍生品估值的投资组合优化问题视为一类随机控制问题，并基于滤波理论和动态规划原理进行了分析。特别是在大偏差控制问题上，引入了考虑下侧风险最小化的新方面，得到了对偶定理等显著结果。

We considered the portfolio optimization problems related to expected utility maximization and valuation of the derivatives as certain kinds of stochastic control problems and developed analysis based on filtering theory and the dynamic programming principles. In particular, we obtained notable results e.g. duality theorems etc., on the large deviation control problems by bringing new aspects in considering down side risk minimization.