A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk

TL;DR

This paper develops a multidimensional exponential utility indifference pricing model for non-traded assets with default risk, providing a semigroup approximation and applying it to counterparty risk in incomplete markets.

Contribution

It introduces a novel splitting method with proven convergence and rate analysis for utility indifference pricing in complex multidimensional settings.

Findings

Convergence of the splitting method is established.

A semigroup approximation for the pricing model is derived.

Application to counterparty risk demonstrates practical relevance.

Abstract

This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitting method, whose convergence is proved based on the Barles-Souganidis monotone scheme, and the convergence rate is derived based on Krylov's shaking the coefficients technique. We apply our methodology to study the counterparty risk of derivatives in incomplete markets.