A Monte Carlo method for exponential hedging of contingent claims
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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.