Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps

Abstract

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced.