Probability Premium and Attitude Towards Probability

TL;DR

This paper introduces a new concept of attitude towards probability based on a generalized probability premium, analyzing its order and implications in risk sharing within different utility models.

Contribution

It develops a novel framework for understanding attitude towards probability and distinguishes between first-order and second-order phenomena in economic models.

Findings

Rank-dependent utility models typically show first-order attitude towards probability.

Dual theory with smooth probability weighting functions exhibits second-order attitude.

Local approximation of probability premium clarifies the nature of attitude towards probability.

Abstract

Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971) probability premium, we introduce a new concept of attitude towards probability. We illustrate in a problem of risk sharing that whether attitude towards probability is a first-order or second-order phenomenon has important economic applications. By developing a local approximation to the probability premium, we show that the canonical rank-dependent utility model usually exhibits attitude towards probability of first order, whereas under the dual theory with smooth probability weighting functions attitude towards probability is a second-order trait.