Stochastic Dominance Under Independent Noise
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) 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.
© 2020 by The University of Chicago. Accepted: July 22, 2019. Electronically published April 6, 2020. We are grateful to the editor and the referees for their comments and suggestions. We also thank Kim Border, Simone Cerreia-Vioglio, Jakša Cvitanic, Ed Green, Elliot Lipnowski, Massimo Marinacci, Doron Ravid, and Xiaosheng Mu as well as seminar audiences at the Workshop on Information and Social Economics at Caltech, the University of Chile, Princeton University, and the Stony Brook International Conference on Game Theory. All errors and omissions are our own. Tamuz was supported by a grant from the Simons Foundation (419427).
Accepted Version - fosd.pdf
Submitted - 1807.06927.pdf