Risk-sensitive portfolio optimization with transaction costs

Abstract

We develop methods of risk-sensitive impulsive control theory in order to solve an optimal asset allocation problem with transaction costs and a stochastic interest rate. The optimal trading strategy and the risk-sensitized expected exponential growth rate of the investor’s portfolio are characterized in terms of a non-linear quasi-variational inequality. This problem can then be interpreted as the ergodic Isaac–Hamilton–Jacobi equation associated with a min–max problem. We use a numerical method based on an extended two-stage policy iteration algorithm for min–max problems and provide numerical results for the case of two assets and one factor that is a Vasicek interest rate.