Optimal initial capital induced by the optimized certainty equivalent

Abstract

This paper proposes the notion of optimal initial capital (OIC) induced by the optimized certainty equivalent (OCE), as discussed in Ben-Tal and Teboulle (1986) and Ben-Tal and Teboulle (2007). It also investigates the properties of the OIC with various types of utility functions. It is shown that the OIC can be a monetary utility function (negative value of risk measure) for future payoffs with the decision maker’s concrete criteria in the background.