Minimal Quantile Functions Subject to Stochastic Dominance Constraints

TL;DR

This paper develops a method to find minimal quantile functions under stochastic dominance constraints, linking it to the Skorokhod problem and applying it to risk minimization in finance.

Contribution

It introduces an explicit solution for SSD-minimal quantile functions under combined FSD and SSD constraints, connecting to the Skorokhod problem and financial risk management.

Findings

Explicit SSD-minimal quantile function solution derived.

Connection established between stochastic dominance and the Skorokhod problem.

Application demonstrated in a financial risk minimization context.

Abstract

We consider a problem of finding an SSD (second-order stochastic dominance)-minimal quantile function subject to the mixture of FSD (first-order stochastic dominance) and SSD constraints. The SSD-minimal solution is explicitly worked out and has a close relation to the Skorokhod problem. This result is then applied to explicitly solve a risk minimizing problem in financial economics.