Quantitative Stability and Empirical Approximation of Risk-Averse Models Induced by Two-Stage Stochastic Programs with Full Random Recourse

Abstract

In this paper, we consider the quantitative stability analysis and empirical approximation of risk-averse models induced by two-stage stochastic programs with full random recourse. We first establish the quantitative stability under the mean-coherent risk measure framework and the expected utility framework, respectively, under suitable probability metrics. Based on the obtained quantitative stability results, we then investigate the empirical approximation to these models, and estimate the rates of convergence for the optimal value and optimal solution set with the aid of Ky Fan distance.