Generalised Means of Simple Utility Functions with Risk Aversion

The paper examines the properties of a generalised mean of simple utilities each displaying risk aversion, that is, with first derivative positive and second derivative negative. It proves the mean is itself a valid utility function with the appropriate signs for derivatives and investigates risk aversion properties. It shows that simple component utilities, each of which may have quite restricted risk aversion properties, can be parsimoniously combined through the generalised mean formula to give a much more versatile utility function.

The Pearson system of utility functions

This paper describes a parametric family of utility functions for decision analysis. The parameterization is obtained by embedding the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. We also describe an alternative technique to estimate the four parameters from elicited utilities, which is simpler and easier to implement than standard fitting by minimization of the mean quadratic error.coefficient of risk aversion, elicitation of preferences under risk, expected utility, HARA utility functions, Pearson system of distributions, prospect theory, probability weighting function, target- based decisions.

Cumulative Prospect Theory for Parametric and Multiattribute Utilities

In cumulative prospect theory models, different behavior concerning gains and losses is per-mitted. For gains different decision weights are assigned than for losses, and the shape of utility can reveal loss aversion. Decision analyses concentrate on both, the capacities, which determine the decision weights, and the nature of utility. This paper focuses on linear/exponential, power and multilinear utility for decision models under uncertainty. Simple preference axioms are for-mulated for a representation by a cumulative prospect theory function. All models share the following axioms: weak ordering, continuity, monotonicity and tail independence. We first show that in their presence constant absolute (proportional) risk aversion implies linear/exponential (power) utility. Then, in the multiattribute case, considering (mutual) utility independence, it is shown that the utility function is (additive/multiplicative) multilinear.mathematical economics and econometrics ;

Generalised Means of Simple Utility Functions with Risk Aversion

The paper examines the properties of a generalised mean of simple utilities each displaying risk aversion, that is, with first derivative positive and second derivative negative. It proves the mean is itself a valid utility function with the appropriate signs for derivatives and investigates risk aversion properties. It shows that simple component utilities, each of which may have quite restricted risk aversion properties, can be parsimoniously combined through the generalised mean formula to give a much more versatile utility function

Generalised Means of Simple Utility Functions with Risk Aversion

The paper examines the properties of a generalised mean of simple utilities each displaying risk aversion, that is, with first derivative positive and second derivative negative. It proves the mean is itself a valid utility function with the appropriate signs for derivatives and investigates risk aversion properties. It shows that simple component utilities, each of which may have quite restricted risk aversion properties, can be parsimoniously combined through the generalised mean formula to give a much more versatile utility function

Reconciling Introspective Utility with Revealed Preference: Experimental Arguments Based on Prospect Theory

In an experiment, choice-based utilities are derived from choices under risk, and choiceless utilities from introspective strength-of-preference judgments. The well-known inconsistencies of risky utility, when analyzed through expected utility, are resolved by means of prospect theory. A consistent cardinal utility index for risky choice results. Remarkably, however, this cardinal index agrees well with the choiceless utilities. This finding suggests a relation between a choice-based and a choiceless concept. Such a relation would imply that direct judgments can provide useful data for economics, and can reinforce the revealed-preference approach. Implications for the classical debate on ordinal versus cardinal utility are discussed.This is a preprint of an article to be published in Journal of Econometric

The Pearson system of utility functions

This paper describes a parametric family of utility functions for decision analysis. The parameterization embeds the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions can have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. The paper also describes an alternative technique to estimate the four parameters from elicited utilities, which is simpler than standard fitting by minimization of the mean quadratic error