An Optimal Investment Problem under Correlated Noises: Risk-Sensitive Stochastic Control Approach

Abstract: This paper is concerned with an optimal investment problem under correlated noises in the financial market, and the expected utility functional is hyperbolic absolute risk aversion (HARA) with the exponent $\gamma\neq0$. The problem can be reformulated as a risk-sensitive stochastic control problem. A new stochastic maximum principle is obtained first, where the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter and the correlation coefficient. The optimal investment strategy is obtained explicitly in a state feedback form via the solution to a certain Riccati equation, under the risk-seeking case. Numerical simulation and figures are given to illustrate the sensitivity for the optimal investment strategy, with respect to the risk-sensitive parameter and the correlation coefficient.