A Monte Carlo method for exponential hedging of contingent claims

TL;DR

This paper introduces a Monte Carlo method for exponential utility-based hedging of contingent claims, simplifying dynamic programming in incomplete markets by learning optimal strategies from simulated data.

Contribution

It presents a novel Monte Carlo algorithm inspired by Longstaff-Schwartz for exponential utility hedging, enhancing practicality and flexibility in incomplete market scenarios.

Findings

Effective learning of optimal hedging strategies from simulated data

Simplifies complex dynamic programming in utility-based pricing

Demonstrates flexibility in incomplete markets

Abstract

Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming, which in practise can be difficult to implement. This article presents a Monte Carlo approach to optimal portfolio problems for which the dynamic programming is based on the exponential utility function U(x)=-exp(-x). The algorithm, inspired by the Longstaff-Schwartz approach to pricing American options by Monte Carlo simulation, involves learning the optimal portfolio selection strategy on simulated Monte Carlo data. It shares with the LS framework intuitivity, simplicity and flexibility.