The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value

Bar Light, Andres Perlroth

Published 2019-08-18Version 1

In this paper we provide a novel family of stochastic orders, which we call the $\alpha,[a,b]$-convex decreasing and $\alpha,[a,b]$-concave increasing stochastic orders, that generalizes second order stochastic dominance. These stochastic orders allow us to compare two lotteries, where one lottery has a higher expected value and is also riskier than the other lottery. The $\alpha,[a,b]$-convex decreasing stochastic orders allow us to derive comparative statics results for applications in economics and operations research that could not be derived using previous stochastic orders. We apply our results in consumption-savings problems, self-protection problems, and in a Bayesian game.