Professor of Decision Sciences
Choice Between Lotteries; Mean and Variance; First-Order Almost-Stochastic Dominance; Marginal Utility; Sharpe Ratio; Omega Ratio
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?The authors provide such a ranking by bounding how much marginal utility can change. Such bounds enable the authors to rank all distributions with given means and variances by first-order almost-stochastic dominance.The authors show how their 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.