Technical Note—Ranking Distributions When Only Means and Variances Are Known

Alfred Müller, Marco Scarsini, Ilia Tsetlin () and Robert L. Winkler ()
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Ilia Tsetlin: INSEAD, Singapore, Singapore 138676
Robert L. Winkler: Fuqua School of Business, Duke University, Durham, North Carolina 27708

Operations Research, 2022, vol. 70, issue 5, 2851-2859

Abstract: 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.

Keywords: Decision Analysis; choice between lotteries; mean and variance; first-order almost-stochastic dominance; marginal utility; Sharpe ratio; Omega ratio (search for similar items in EconPapers)
Date: 2022
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