Numerical aspects of adapted optimal transport
Abstract
Recent work has established that the adapted Wasserstein distance satisfies many desirable theoretical properties for multi-period market models, guaranteeing for instance robustness against model misspecification and geodesic closedness of the set of martingale models. To actually benefit from such properties in practice, one requires ways to numerically calculate adapted optimal transport problems. The goal of this talk is to present various computational tools aimed at working with adapted optimal transport in practice. Among others, we show feasibility of discrete approximations for continuous problems and how to control errors introduced by regularization methods. Extending the classical theory, we introduce a variant of Sinkhorn's algorithm to solve the regularized problem and establish its exponential convergence. We will illustrate geometric aspects of the adapted optimal transport problem by numerically calculating model ensembles of different martingale models. Based on joint work with Gudmund Pammer.
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