Reference-Based Almost Stochastic Dominance Rules with Application in Risk-Averse Optimization

• Main Authors: Hu, Jian, Stepanyan, Gevorg
• Format: Journal Article
• Language: English
• Published: 24-12-2015
• Subjects: Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.1512.07953

Stochastic dominance is a preference relation of uncertain prospect defined
over a class of utility functions. While this utility class represents basic
properties of risk aversion, it includes some extreme utility functions rarely
characterizing a rational decision maker's preference. In this paper we
introduce reference-based almost stochastic dominance (RSD) rules which well
balance the general representation of risk aversion and the individualization
of the decision maker's risk preference. The key idea is that, in the general
utility class, we construct a neighborhood of the decision maker's individual
utility function, and represent a preference relation over this neighborhood.
The RSD rules reveal the maximum dominance level quantifying the decision
maker's robust preference between alternative choices. We also propose RSD
constrained stochastic optimization model and develop an approximation
algorithm based on Bernstein polynomials. This model is illustrated on a
portfolio optimization problem.