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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 718714, 15 pages
Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game Problem
1School of Mathematical Sciences, Ocean University of China, Qingdao 266003, China
2School of Mathematics, Shandong University, Jinan 250100, China
Received 4 October 2012; Accepted 10 December 2012
Academic Editor: Guangchen Wang
Copyright © 2012 Lifeng Wei and Zhen Wu. 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.
- E. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems & Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
- D. Duffie and L. G. Epstein, “Stochastic differential utility,” Econometrica, vol. 60, no. 2, pp. 353–394, 1992.
- N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M. C. Quenez, “Reflected solutions of backward SDE's, and related obstacle problems for PDE's,” The Annals of Probability, vol. 25, no. 2, pp. 702–737, 1997.
- J. Cvitanic and I. Karatzas, “Backward SDE's with reflection and Dynkin games,” The Annals of Probability, vol. 24, no. 4, pp. 2024–2056, 1996.
- S. Hamadène and J.-P. Lepeltier, “Zero-sum stochastic differential games and backward equations,” Systems & Control Letters, vol. 24, no. 4, pp. 259–263, 1995.
- G. Wang and Z. Yu, “A Pontryagin's maximum principle for non-zero sum differential games of BSDEs with applications,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1742–1747, 2010.
- G. Wang and Z. Yu, “A partial information non-zero sum differential game of backward stochastic differential equations with applications,” Automatica, vol. 48, no. 2, pp. 342–352, 2012.
- N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
- S. Hamadène, “Mixed zero-sum stochastic differential game and American game options,” SIAM Journal on Control and Optimization, vol. 45, no. 2, pp. 496–518, 2006.
- E. Pardoux, “BSDE's, weak convergence and homogenization of semilinear PDE's,” in Nonlinear Analysis, Differential Equations and Control, F. H. Clarke and R. J. Stern, Eds., vol. 528, pp. 503–549, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
- V. E. Benes, “Existence of optimal strategies based on specified information, for a class of stochastic decision problems,” SIAM Journal on Control and Optimization, vol. 8, pp. 179–188, 1970.
- J. P. Lepeltier, A. Matoussi, and M. Xu, “Reflected BSDEs under monotonicity and general increasing growth conditions,” Advanced in Applied Probability, vol. 37, pp. 134–159, 2005.
- N. El Karoui, E. Pardoux, and M. C. Quenez, “Reflected backward SDEs and American options,” in Numerical methods in Finance, L. C. G. Rogers and D. Talay, Eds., vol. 13, pp. 215–231, Cambridge University Press, Cambridge, Mass, USA, 1997.
- S. Hamadène and I. Hdhiri, “Backward stochastic differential equations with two distinct reflecting barriers and quadratic growth generator,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2006, Article ID 95818, 28 pages, 2006.