Strong Convexity in Stochastic Programs with Deviation Risk Measures

TL;DR

This paper establishes conditions under which certain risk measures in two-stage stochastic programs exhibit strong convexity, extending previous results from risk-neutral models to more complex risk measures.

Contribution

It provides sufficient conditions for strong convexity of expected excess and upper semideviation in two-stage stochastic programs with linear recourse.

Findings

Expected excess and upper semideviation are strongly convex under new conditions.

Extends strong convexity results from risk-neutral to risk-averse models.

Applicable to models with complete linear recourse and random right-hand side.

Abstract

We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand side. This work extends results on strong convexity of risk-neutral models.