Alfred Müller, Marco Scarsini, Ilia Tsetlin, Robert L. Winkler
Consider a choice between two random variables, for which only means and variances are known. Is it possible to rank them by putting some constraints on risk preferences? We provide such a ranking by bounding how much marginal utility can change. Such bounds enable us to rank all distributions with given means and variances by first-order almost-stochastic dominance. We show how our results can be used to compare a risky project and a sure payoff and also provide a new connection between the Sharpe and Omega ratios from finance. © 2021 INFORMS.
Department Mathematik, Universität Siegen, Siegen, 57072, Germany; Dipartimento di Economia e Finanza, Luiss University, Roma, 00197, Italy; INSEAD, Singapore, 138676, Singapore; Fuqua School of Business, Duke University, Durham, 27708, NC, United States
