Mean-semivariance Portfolio Selection Based On An Incomplete Market With External Risk Factors Of Non-Gaussian OU Processes Under Probability Distortion

We study a mean-variance portfolio selection problem via optimal feedback con-trol based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black-Scholes market. Then, We formulate and study a mean-semivariance portfolio selection problem in continuous time when the probability is distorted by a nonlinear transformation. More precisely, there are three steps involved. First, we simplify the problem by the variance-optimal martin-gale measure and the quantile formulation. Second, we give necessary and sufficient conditions for the feasibility. Third, we give necessary and sufficient conditions for the existence of optimal strategies, respectively, and present the general form of optimal solutions when they exist.