Risk aversion for nonsmooth utility functions

Risk Aversion for Nonsmooth Utility Functions

This paper generalizes the notion of risk aversion for functions which are not necessarily differentiable nor strictly concave. Using an approach based on superdifferentials, we define the notion of a risk aversion measure, from which the classical absolute as well as relative risk aversion follows as a RadonNikodym derivative if it exists. Using this notion, we are able to compare risk aversio...

Modeling non-monotone risk aversion using SAHARA utility functions

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk-averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under S...

Reexamining Utility Functions for Normative Risk Analysis: Cara Utility and Gain Aversion

Expected Utility and Risk Aversion

This reading describes how people’s aversion to risk affects the decisions they make about investment. Basically, the concepts used to do this analysis emerge naturally when people have expected utility preferences, but not otherwise. So, it illustrates one important way that expected utility is applied. This analysis also makes it possible to illustrate how to do comparative statics. Comparati...

Risk Aversion Asymptotics for Power Utility Maximization

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to in nity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential an...