Why Investors Buy Insurance and Try Their Luck with Lotteries as Well?

Abstract

In this paper, we develop a new stochastic dominance (SD) theory for investors with AD utility that consists of both risk-averse and risk-seeking components. Based on the SD theory we developed in our paper, we find a new solution to answer the observation posed by Friedman and Savage (1948) that people could buy insurance and try their luck with lotteries as well. We find that investors with AD utility will buy both insurance and try their luck with lotteries to get higher expected utility. We find that investors with AD utility will buy both bonds and stocks and both bonds and futures to get higher expected utility. In addition, we develop some properties, including expected-utility maximization, hierarchy, transitivity, and diversification, for the new SD theory for investors with AD utility.

Keywords: Stochastic Dominance, Risk Aversion, Risk Seeking, Utility Function, More Risky Asset, Less Risky Asset

JEL Classification: D81, G11