Hedging under worst-case-scenario in a market driven by time-changed L\'evy noises

TL;DR

This paper develops a worst-case-scenario hedging strategy in incomplete markets driven by time-changed Le9vy noises, using stochastic differential games and backward SDEs to address model uncertainty.

Contribution

It introduces a novel approach to hedging under model uncertainty in markets driven by complex stochastic processes, considering non-self-financing strategies and multiple information flows.

Findings

Hedging strategies are effective under worst-case scenarios.

Comparison of information flows shows different hedging outcomes.

The framework extends to incomplete markets with complex noise models.

Abstract

In an incomplete market driven by time-changed L\'evy noises we consider the problem of hedging a financial position coupled with the underlying risk of model uncertainty. Then we study hedging under worst-case-scenario. The proposed strategies are not necessarily self-financing and include the interplay of a cost process to achieve the perfect hedge at the end of the time horizon. The hedging problem is tackled in the framework of stochastic differential games and it is treated via backward stochastic differential equations. Two different information flows are considered and the solutions compared.