Sensitivity of multiperiod optimization problems in adapted Wasserstein distance

TL;DR

This paper investigates how small probabilistic model changes, measured via adapted Wasserstein distance, impact multi-period stochastic optimization and stopping problems, providing explicit first-order approximations.

Contribution

It introduces explicit first-order approximation formulas for the sensitivity of multi-period optimization problems under adapted Wasserstein distance.

Findings

Derived explicit first-order sensitivity formulas.

Applicable to expected utility maximization.

Provides insights into model robustness in stochastic optimization.

Abstract

We analyze the effect of small changes in the underlying probabilistic model on the value of multi-period stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit first-order approximations for both problems. Expected utility maximization is discussed as a special case.