Stochastic Dominance Under Independent Noise

TL;DR

This paper investigates how independent background risks influence stochastic dominance relations among gambles, revealing that such risks can alter the ranking of lotteries and providing new axiomatizations for mean-variance preferences.

Contribution

It demonstrates that independent background risk can reverse stochastic dominance orderings and offers a new axiomatization of mean-variance preferences.

Findings

Background risk can overturn first-order stochastic dominance rankings.

Results extend to second-order stochastic dominance.

Provides a simple axiomatization of mean-variance preferences.

Abstract

Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor risk, house price risk, etc.) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second order stochastic dominance, and show how they lead to a novel, and elementary, axiomatization of mean-variance preferences.