Risk-averse and Distributionally Robust Multistage Stochastic Optimization

Duque Villarreal, Daniel

doi:https://doi.org/10.21985/n2-67g3-9104

Work

Risk-averse and Distributionally Robust Multistage Stochastic Optimization

Public

Download PDF

Download All Files (.zip)

This dissertation investigates a number of models and algorithms in the context of optimization under uncertainty. The focus is on risk-averse optimization, where risk aversion is modeled via stochastic dominance, utility theory, and distributionally robust optimization. We first investigate an investment model with fixed contribution rates, optimize asset-allocation decisions in a closed-loop policy, and compare the results with the default open-loop policy for the Chilean pension system. Our results indicate that the Chilean default policy has good overall performance, but specific closed-loop policies have a higher probability of achieving desired retirement goals and can reduce the expected shortfall at retirement. Next, we consider a multi-stage stochastic linear program that lends itself to solution by stochastic dual dynamic programming (SDDP). In this context, we consider a distributionally robust variant of the model with a finite number of realizations at each stage. Distributional robustness is with respect to the probability mass function governing these realizations. We describe a computationally tractable variant of SDDP to handle this model using the Wasserstein distance to characterize distributional uncertainty. Finally, we explore more general variants of distributionally robust formulations in the context of two-stage stochastic programs. Specifically, we consider variants of the model in which probability distributions are no longer restricted to a finite number of realizations, and instead, we allow distributions to be defined on uncountable support sets. We again focus on the Wasserstein distance under a p-norm, and extend some of the results to the optimal quadratic transport distance. We study variants with both unbounded and bounded support sets, and provide guidance regarding which models are meaningful in the sense of yielding robust solutions. The models, algorithms, and applications that we cover provide a broad overview of modern topics in risk-averse optimization.

Creator