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Mathematical Problems in Engineering
Volume 2013, Article ID 165727, 9 pages
Research Article

Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
2Department of Mathematics and Statistics, Curtin University, Perth, WA 6102, Australia

Received 16 January 2013; Revised 22 March 2013; Accepted 13 April 2013

Academic Editor: Guangchen Wang

Copyright © 2013 Xinfeng Ruan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.