Stability of the Weak Martingale Optimal Transport Problem

TL;DR

This paper establishes the stability of weak martingale optimal transport (WMOT), crucial for financial applications with imprecise data, and explores its implications for superreplication bounds, stretched Brownian motion, and monotonicity principles.

Contribution

It proves the stability of WMOT and applies this to key financial models and principles, extending the theoretical framework of martingale optimal transport.

Findings

Stability of WMOT established

Superreplication bounds for VIX futures are stable

Monotonicity principle for WMOT derived

Abstract

While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this corresponds to weak martingale optimal transport (WMOT). In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of stretched Brownian motion and we derive a monotonicity principle for WMOT.