Ranking Distributions when only Means and Variances are Known

INSEAD Working Paper No. 2020/36/DSC

Forthcoming in Operations Research

15 Pages Posted: 21 Aug 2019 Last revised: 5 Aug 2020

See all articles by Alfred Müller

Alfred Müller

University of Siegen

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza

Ilia Tsetlin

INSEAD

Robert L. Winkler

Duke University - Fuqua School of Business

Date Written: August 5, 2020

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: stochastic dominance, utility, risk. Probability: distribution comparisons

Suggested Citation

Müller, Alfred and Scarsini, Marco and Tsetlin, Ilia and Winkler, Robert L., Ranking Distributions when only Means and Variances are Known (August 5, 2020). INSEAD Working Paper No. 2020/36/DSC, Forthcoming in Operations Research, Available at SSRN: https://ssrn.com/abstract=3440103 or http://dx.doi.org/10.2139/ssrn.3440103

Alfred Müller

University of Siegen ( email )

Department Mathematik
Walter-Flex-Str. 3
57068 Siegen
Germany

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Ilia Tsetlin (Contact Author)

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Robert L. Winkler

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

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