Session: Distributional Shift and Systemic Risk
Chair: Lai Tian
Cluster:
Talk 1: Sample-average approximations for systemic risk measures
Speaker: Çağın Ararat
Abstract: We investigate the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity properties and value-at-risk applied as a monetary risk measure. Our focus is on the theoretical convergence of its SAA under Wijsman and Hausdorff topologies for closed sets. After building the general theory, we provide an in-depth study of an important special case where the aggregation function is defined based on the Eisenberg-Noe network model. In this case, we provide mixed-integer programming formulations for calculating the SAA sets via their weighted-sum and norm-minimizing scalarizations. When value-at-risk is replaced with expectation, we also provide lower bounds on the required sample size for a sufficiently close SAA with high probability. Based on joint works with Wissam AlAli and Nurtai Meimanjan.
Talk 3: Stabilizing Stochastic Programs with Rockafellian Relaxation: Theoretical Results and Chance-Constrained Applications
Speaker: Lai Tian
Abstract: Solutions of a stochastic optimization problem tend to change disproportionally under small changes to its probability distribution. This sensitivity is particularly concerning, as it is virtually impossible to identify the “correct” distribution in real-world applications. In this talk, we demonstrate how Rockafellian relaxations provide a principled and effective approach to improving the stability of solutions under distributional changes. Unlike previous efforts that primarily focus on finite or discrete distributions, our framework accommodates general Borel probability measures and handles discontinuous integrands, such as those arising in chance-constrained formulations. These advances broaden the scope of robust solution techniques in modern stochastic optimization.
