Optimal Investment Strategy for Kinked Utility Maximization: Covered Call Option Strategy

Abstract

This paper describes optimal investment strategies for kinked utility functions. One example is a CRRA utility function with a kink at a maximum wealth, which leads a covered call “ like ” strategy and the other is a CRRA utility function with a kink at a minimum wealth, which leads a protective put “ like ” strategy. This paper introduces analytic mathematical solutions providing a mathematical explanation of a dual utility where Black-Sholes assumption is utilized in the solutions. The intuitive solutions are clear for cases of those kinked utilities but minute mathematical explanation is described. Also a numerical simulation is performed for a covered call like strategy case.