Utility indifference pricing and the Aumann-Serrano performance index (Q2304208)

The authors propose a performance index based on the economic index of riskiness for gambles by \textit{R. J. Aumann} and \textit{R. Serrano} [J. Polit. Econ. 116, No. 5, 810--836 (2008; Zbl 1341.91040)]. In particular, the paper considers a new class of gambles \(g\), where \(E[g]<0\) and \(P(g>0)>0\). This class had not yet been included in the literature. After presenting definitions and properties of the risk-sensitive value measure (RSVM) and, specifically, the utility indifference price with the exponential utility function, the paper provides a definition of the inner rate of risk aversion (IRRA) and a sufficient condition of the existence and uniqueness of the negative IRRA. Then a relationship between the IRRA and the Aumann and Serrano performance index is investigated. Some empirical examples show how the results presented are applicable to many gambles in reality.