# American Institute of Mathematical Sciences

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October  2008, 4(4): 783-799. doi: 10.3934/jimo.2008.4.783

## A power penalty approach to american option pricing with jump diffusion processes

 1 Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060, China 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong 3 Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received  February 2008 Revised  August 2008 Published  November 2008

This paper is devoted to develop a power penalty method for pricing the American option model where the underlying asset is assumed to follow a jump diffusion process. With the help of the linear complementarity problem and variational inequalities, we propose a power penalty approach for a partial integro-differential complementarity problem, which is the mathematical model of pricing the American option with a jump diffusion process. The convergence analysis of the power penalty approach is established. Finally, based on the finite element discretization, a numerical scheme is developed to solve the penalized problem and the numerical tests are designed to illustrate the efficiency of this method.
Citation: Kai Zhang, Xiaoqi Yang, Kok Lay Teo. A power penalty approach to american option pricing with jump diffusion processes. Journal of Industrial & Management Optimization, 2008, 4 (4) : 783-799. doi: 10.3934/jimo.2008.4.783
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