Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate

Abstract

In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

The Study of Mean-Variance Risky Asset Management with State-Dependent Risk Aversion under Regime Switching Market

“…Previous researches in this area are classified for the endogenous habit formation [2], the classic constant relative risk aversion (CRRA) by Yu and Yuan [4], the hyperbolic discounting [3], and the utilities like the mean-variance utility proposed by Li et al [5]. In recent paper by Li et al [6], the analytical solution portfolio optimization problem involving stochastic shortterm interest rates is provided, which can be controlled by the mean-variance utility function with state dependent risk aversion (SDRA). The paper [6] uses the Nash equilibrium for the subgame strategy to concrete analytical expressions of value function and control policy of equilibrium and figure out under the condition of the stochastic short-term interest rates, how do investors with "natural risk aversion" achieve optimal control policies by simplifying financial settings.…”