Utility indifference pricing and the Aumann–Serrano performance index

Abstract

A performance index based on the economic index of riskiness by Aumann and Serrano (2008) can be derived from an index based on the utility indifference price with the exponential utility function. The exponential utility function is a special utility function and relevant when the associated investor is risk averse as well as risk loving. The index based on the utility indifference price with the exponential utility function becomes an index for the random variable g of gambles with the property E[g]>0 and P(g<0)>0 when the investor is risk averse and an index for the random variable g of gambles with the property E[g]<0 and P(g>0)>0 when the investor is risk loving. We provide sufficient conditions for the existence and uniqueness of the index when the investor is risk averse and risk loving.