Cumulative Prospect Theory with Generalized Hyperbolic Skewed $t$ Distribution

We investigate a one-period portfolio optimization problem of a cumulative prospect theory (CPT) investor with multiple risky assets and one risk-free asset. The returns of the multiple risky assets follow a multivariate generalized hyperbolic (GH) skewed $t$ distribution. We obtain a three-fund separation result comprised of two risky portfolios and the risk-free asset. Furthermore, we reduce the high-dimensional optimization problem to two 1-dimensional optimization problems in order to derive the optimal portfolio. We show that the optimal portfolio composition changes as some of the investor-specific parameters change. The skewness of the stock return distribution is observed to have a considerable impact on the distribution of the CPT investor's wealth deviation, leading to a more conservative investment decision.