Optimal portfolio in the presence of transaction costs and convex risk measure

Abstract

We analyze the optimal portfolio selection problem of maximizing the utility of an agent who invests in a stock and a money market account in the presence of transaction costs. The stock price follows a geometric process. The preference of the investor is assumed to follow the constant relative risk aversion (CRRA). We further investigate the risk minimizing portfolio through a zero-sum stochastic differential game (SDG). To solve this two-player SDG we use the Hamilton–Jacobi–Bellman–Isaacs (HJBI) for general zero-sum SDG in a jump setting.