Dynamic Mean-Downside Risk Portfolio Selection Problem with Stochastic Interest Rate in Continuous-Time

Even though a consensus has been reached a long time ago that the interest rate is a stochastic process, most of the existing works on dynamic mean-downside risk portfolio selection still focus on a deterministic interest rate. This work studies a dynamic mean-downside risk portfolio selection problem with a stochastic interest rate in a continuous-time financial market. Specifically, we choose the lower-partial moments(LPM), value-at-risk (VaR), and conditional value-at-risk(CVaR) to model our downside risk measures in the Vasicek interest rate model. 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 a stochastic interest rate. The results suggest that the higher the degree of negative correlation, the better the performance of the portfolio valued by mean-downside risk framework when the other market opportunity set is the same