Robust Superhedging with Jumps and Diffusion

TL;DR

This paper develops a robust superhedging framework incorporating jump processes and diffusion, establishing a duality and optimal strategies in a nondominated setting, with applications to nonlinear Lévy processes.

Contribution

It introduces a nondominated optional decomposition theorem and derives a superhedging duality for models with jumps and diffusion, extending existing theories.

Findings

Established a nondominated optional decomposition theorem.

Derived a robust superhedging duality.

Proved existence of optimal superhedging strategies.

Abstract

We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the existence of an optimal superhedging strategy for general contingent claims. We illustrate the main results in the framework of nonlinear L\'evy processes.