Robust Hedging of American Options via Aggregated Snell Envelopes

TL;DR

This paper develops a robust hedging framework for American options by constructing an aggregator for Snell envelopes in complex market models, ensuring duality and minimal strategies under uncertainty.

Contribution

It introduces a novel aggregation method for Snell envelopes in nondominated models, enabling robust hedging duality and minimal strategies for American options.

Findings

Established a robust hedging duality for American options.

Proved the existence of minimal hedging strategies.

Applicable to models with jumps and non-vanishing diffusion.

Abstract

We construct an aggregator for a family of Snell envelopes in a nondominated framework. We apply this construction to establish a robust hedging duality, along with the existence of a minimal hedging strategy, in a general semi-martingale setting for American-style options. Our results encompass continuous processes, or processes with jumps and non-vanishing diffusion. A key application is to financial market models, where uncertainty is quantified through the semi-martingale characteristics.