Sensitivity of multiperiod optimization problems in adapted Wasserstein distance

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.

final version, accepted for publication in SIAM J. Financial Math