Distorted stochastic dominance: a generalized family of stochastic orders

TL;DR

This paper introduces a generalized family of stochastic dominance relations, called H-distorted stochastic dominance, which can better capture decision makers' risk preferences and is computationally simple, especially with power distortion functions.

Contribution

It defines and analyzes a new family of stochastic orders based on distortion functions, extending traditional stochastic dominance concepts and focusing on power distortions for simplicity.

Findings

Introduces H-distorted stochastic dominance as a continuum of order relations.

Characterizes distorted stochastic dominance via distortion functions and expectations.

Highlights the computational and interpretative advantages of power distortion functions.

Abstract

We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a decision maker's preferences in terms of risk aversion and may be used in those situations in which a strong order does not have enough discriminative power, whilst a weaker one is poorly representative of some classes of decision makers. In particular, we focus on the class of power distortion functions, yielding power-distorted stochastic dominance, which seems to be particularly appealing owing to its computational simplicity and some interesting statistical interpretations. Finally, we characterize distorted stochastic dominance in terms of distortion functions yielding isotonic classes of distorted expectations.