Quantile hedging for an insider

TL;DR

This paper studies quantile hedging strategies for an insider with extra market information, extending existing models to account for an informed agent and providing explicit solutions in the Black-Scholes framework.

Contribution

It extends quantile hedging theory to insiders by incorporating initial filtration enlargement and solves the problem explicitly in the Black-Scholes model.

Findings

Explicit solutions for insider quantile hedging in Black-Scholes.

Extension of existing models to include informed agents.

Application of equivalent martingale measures in the insider context.

Abstract

In this paper we consider the problem of the quantile hedging from the point of view of a better informed agent acting on the market. The additional knowledge of the agent is modelled by a filtration initially enlarged by some random variable. By using equivalent martingale measures introduced in Amendinger (2000) and Amendinger, Imkeller and Schweizer (1998) we solve the problem for the complete case, by extending the results obtained in F{\"o}llmer and Leukert (1999) to the insider context. Finally, we consider the examples with the explicit calculations within the standard Black-Scholes model.