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April  2008, 4(2): 227-246. doi: 10.3934/jimo.2008.4.227

Finite difference approximation for stochastic optimal stopping problems with delays

Mou-Hsiung Chang 1, , Tao Pang 2, and  Moustapha Pemy 3,

1. 

Mathematics Division, U. S. Army Research Office, P. O. Box 12211, RTP, NC 27709, United States
2. 

Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205, United States
3. 

Department of Mathematics, Towson University, 7800 York Road, Room 316, Towson, MD 21252-0001, United States

Received  March 2007 Revised  September 2007 Published  April 2008

This paper considers the computational issue of the optimal stopping problem for the stochastic functional differential equation treated in [6] The finite difference method developed by Barles and Souganidis [3] is used to obtain a numerical approximation for the viscosity solution of the infinite dimensional Hamilton-Jacobi-Bellman variational inequality (HJBVI) associated with the optimal stopping problem. The convergence results are then established.
Keywords: finite difference., optimal stopping, stochastic functional differential equations, stochastic control.
Mathematics Subject Classification: Primary: 60A09, 60H30; Secondary: 60G44, 90A1.
Citation: Mou-Hsiung Chang, Tao Pang, Moustapha Pemy. Finite difference approximation for stochastic optimal stopping problems with delays. Journal of Industrial & Management Optimization, 2008, 4 (2) : 227-246. doi: 10.3934/jimo.2008.4.227
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