Ranking Distributions when only Means and Variances are Known
Forthcoming in Operations Research
15 Pages Posted: 21 Aug 2019 Last revised: 5 Aug 2020
Date Written: August 5, 2020
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: stochastic dominance, utility, risk. Probability: distribution comparisons
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