Superhedging duality for multi-action options under model uncertainty with information delay

TL;DR

This paper establishes a duality for superhedging prices of exotic options under model uncertainty with delayed information, extending classical results to more complex, realistic market scenarios.

Contribution

It introduces an enlarged space framework to prove superhedging duality for multi-action options under nondominated model uncertainty with information delay.

Findings

Proves superhedging duality for exotic options with multiple actions.

Shows superhedging price equals model-based price with delayed information.

Extends duality results to settings with information asymmetry and delay.

Abstract

We consider the superhedging price of an exotic option under nondominated model uncertainty in discrete time in which the option buyer chooses some action from an (uncountable) action space at each time step. By introducing an enlarged space we reformulate the superhedging problem for such an exotic option as a problem for a European option, which enables us to prove the pricing-hedging duality. Next, we present a duality result that, when the option buyers action is observed by the seller up to $l$ periods later, the superhedging price equals the model-based price where the option buyer has the power to look into the future for $l$ periods.