A general framework for pricing and hedging under local viability

TL;DR

This paper introduces a novel framework for pricing and hedging derivatives in frictionless markets, applicable even without an equivalent local martingale measure, and establishes a superhedging duality for American options with wealth constraints.

Contribution

It presents a new superhedging duality for American options under wealth negativity and cone constraints, extending existing theories in derivative pricing.

Findings

Superhedging duality for American options with negative wealth processes

Applicable in markets lacking an equivalent local martingale measure

Addresses open questions in derivative pricing theory

Abstract

In this paper, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to exist. Our main results include a new superhedging duality for American options when wealth processes can be negative and trading strategies are subject to a cone constraint. This answers one of the questions raised by Fernholz, Karatzas and Kardaras.