We derive a class of utility functions that are equivalent with respect to a well-defined functional form. We apply a general view of constant relative risk aversion to investigate on different equivalence relations. Then we compare our results with standard applications in economics and finance.

We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the...