Dynamic mean-downside risk portfolio selection with a stochastic interest rate in continuous-time

Abstract

Even though it has long been agreed that the interest rate is driven by a stochastic process, most of the existing studies on dynamic mean-downside risk portfolio optimization problem focuses on deterministic interest rates. This work investigates a continuous-time mean-downside risk portfolio optimization problem with a stochastic interest rate. More specifically, we introduce the Vasicek interest rate model and choose some common downside risk measures to model our risk measures, such as, the lower-partial moments(LPM), value-at-risk(VaR) and conditional value-at-risk(CVaR). By using the martingale method and the inverse Fourier Transformation, we successfully derive the semi-analytical optimal portfolio policies and the optimal wealth processes for the mean-downside risk measures with stochastic interest rate. Finally, we provide some illustrative examples to show how the stochastic interest rate affects the investment behavior of investors with mean-downside risk preferences.