Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance

This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart. But the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter. This result is used to solve a kind of optimal portfolio choice problem and the optimal portfolio choice strategy is obtained. Computational results and figures explicitly illustrate the optimal solution and the sensitivity to the volatility rate parameter.