We give an overview of the studies of stochastic control and filtering theory, tracing the historical situation from Kalman-Bucy filtering, LQG stochastic control theory and their mathematical generalization to nonlinear systems and nonlinear filtering to H^∞ control and risk-sensitive stochastic control. Then we explain how we could formulate portfolio optimization problems for Merton's ICAPM, which are typical ones on mathematical finance, as risk-sensitive stochastic control problems based on understanding the situation, and analyze them by employing the methods established through such studies. Dynamic programming approach to stochastic control and the methods of measure change in nonlinear filtering apply to obtain explicit representation of optimal strategies for the portfolio optimization problems. More other aspects could be seen.
