The computational property of the Aumann–Serrano performance index under risk-averse and risk-loving preference

Abstract

We consider computational aspects of the Aumann–Serrano (AS) performance index proposed by Kadan and Liu (2014). When investors are not only risk averse but also risk loving, the original implicit equation of the AS performance index has in general two solutions of the true index and a pseudo index of zero. This makes it difficult to search for the true index by programs of solving nonlinear equations. On the other hand, an implicit equation of another equivalent performance index based on utility indifference pricing is a continuous and strictly decreasing function, which makes it always easy to find the true index by programs.