An Approximation for Exponential Hedging

Abstract

An optimization problem in mathematical finance, called the exponential hedging problem is addressed. First, the relations between the problem and the backward stochastic differential equation (abbreviated to BSDE) having a quadratic growth term in the drift are reviewed. Next, the asymptotic analysis by Davis (2000) for the problem and the motivation of this paper are stated. Further, with some extensions, his analysis is reinterpreted by using the asymptotic expansion of the BSDE with respect to a small parameter, which suggests an alternative approach to the analysis, and the result on an approximated optimizer is obtained.