Equilibrium strategy for mean–variance–utility portfolio selection under Heston’s SV model

Abstract

This paper considers a mean–variance–utility portfolio problem in which the investor manages her/his wealth by consuming and investing in a financial market consisting of a risk-free bond and a risky asset whose price process follows Heston’s stochastic volatility (SV) model. The objective of the investor is to obtain an equilibrium investment and consumption strategy by maximizing the terminal wealth and the accumulated binary utility function incorporating consumption and income. The semi-closed form expressions for the equilibrium investment and consumption strategy as well as the corresponding value function are derived by solving an extended Hamilton–Jacobi–Bellman system within the game-theoretic framework. Moreover, some numerical experiments are provided to show the effects of model parameters on the equilibrium strategy by adopting the Cobb–Douglas utility function.