publication . Article . 2011

Optimal Selling Rule in a Regime Switching Lévy Market

Pemy, Moustapha;
Open Access
  • Published: 01 Jan 2011 Journal: International Journal of Mathematics and Mathematical Sciences, volume 2,011, pages 1-28 (issn: 0161-1712, eissn: 1687-0425, Copyright policy)
  • Publisher: Hindawi Limited
Abstract
<jats:p>This paper is concerned with a finite-horizon optimal selling rule problem when the underlying stock price movements are modeled by a Markov switching Lévy process. Assuming that the transaction fee of the selling operation is a function of the underlying stock price, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB variational inequalities. A numerical example is presented to illustrate the results.</jats:p>
Subjects
arXiv: Computer Science::Computer Science and Game Theory
free text keywords: Mathematics (miscellaneous), Mathematics, QA1-939, Article Subject

Zhang, Q.. Stock trading: an optimal selling rule. SIAM Journal on Control and Optimization. 2001; 40 (1): 64-87

Pemy, M., Zhang, Q.. Optimal stock liquidation in a regime switching model with finite time horizon. Journal of Mathematical Analysis and Applications. 2006; 321 (2): 537-552 [OpenAIRE]

McKean, H. P.. A free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review. 1960; 60: 32-39

Samuelson, P. A.. Rational theory of warrant pricing. Industrial Management Review. 1995; 6: 13-32

ØKsendal, B.. Stochastic Differential Equations. 1998

Guo, X., Zhang, Q.. Optimal selling rules in a regime switching model. Institute of Electrical and Electronics Engineers Transactions on Automatic Control. 2005; 50 (9): 1450-1455

Krylov, N. V.. Controlled Diffusion Processes. 1980; 14

Pham, H.. Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. Journal of Mathematical Systems, Estimation, and Control. 1998; 8 (1): 1-27

Pemy, M.. Option pricing under regime witching, Ph.D. thesis. 2005

Crandall, M. G., Ishii, H., Lions, P.-L.. User's guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society. 1992; 27 (1): 1-67 [OpenAIRE]

Yin, G. G., Zhang, Q.. Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. 1998; 37

Fleming, W. H., Soner, H. M.. Controlled Markov Processes and Viscosity Solutions. 2006; 25

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