带限制倒向随机微分方程在停时对策中的应用
Constraint BSDE for Stopping Game
DOI: 10.12677/AAM.2018.76087, PDF,    科研立项经费支持
作者: 吴和林：重庆理工大学，重庆
关键词: 倒向随机微分方程；停时对策；限制问题；BSDE； Stopping Game； Constraint Problem
摘要: 本文我们研究了由倒向随机微分方程诱导的非线性g-期望下的Dynkin停时对策问题。在我们的假设之下，我们获得了一组鞍点并由此得出了对策解的存在性。除此之外，我们还讨论了存在限制的情况。我们的结果可以应用到非常一般情形下的美式期权定价问题之中。
Abstract: In this paper, we investigate some kind of Dynkin’s game under n on-linear g-expectation induced by Backward Stochastic Differential Equation (shortly BSDE). Under regular assumptions, a pair of a saddle point is obtained and the existence of the value function follows. The constrained case is also treated in this paper. As an application, we study American game options in very general framework.
文章引用：吴和林. 带限制倒向随机微分方程在停时对策中的应用[J]. 应用数学进展, 2018, 7(6): 723-730. https://doi.org/10.12677/AAM.2018.76087

参考文献

[1] Dynkin, E.B. (1969) Game Variant of a Problem on Optimal Stopping. Soviet Mathematics Doklady, 10, 270-274.
[2] Krylov, N.V. (1971) Control of Markov Processes and W-Spaces. Mathematics of the USSR-Izvestiya, 5, 233-266.
[Google Scholar] [CrossRef] 
[3] Cvitanic, J. and Karatzas, I. (1996) Backward Stochastic Differential Equations with Reflection and Dynkin Games. The Annals of Probability, 4, 2024-2056.
[Google Scholar] [CrossRef] 
[4] Hamadene, S. and Lepeltier, J.-P. (2000) Reflected BSDEs and Mixed Game Problem. Stochastic Processes and their Applications, 85, 177-188.
[Google Scholar] [CrossRef] 
[5] Bensoussan, A. and Friedman, A. (1974) Nonlinear Variational Inequali-ties and Differential Games with Stopping Times. Journal of Functional Analysis, 16, 305-352.
[Google Scholar] [CrossRef] 
[6] Friedman, A. (1973) Stochastic Games and Variational Inequalities. Archive for Rational Mechanics and Analysis, 51, 321-346.
[Google Scholar] [CrossRef] 
[7] Karatzas, I. (1996) A Pathwise Approach to Dynkin Games. Statistics, Probability and Game Theory, 30, 115-125.
[Google Scholar] [CrossRef] 
[8] Karatzas, I. and Wang, H. (2001) Connections between Bounded-Variation Control and Dynkin Games. Optimal Control and Partial Differential Equation, 363-373.
[9] Peng, S.G. and Xu, M.Y. (2010) Reflected BSDE with a Constraint and its Applications in an Incomplete Market. Bernoulli, 16, 614-640.
[Google Scholar] [CrossRef] 
[10] Peng, S.G. (1999) Monotonic Limit Theorem of BSDE and Nonlinear Decomposition Theorem of Doob-Meyer’s Type. Probability Theory and Related Fields, 113, 473-499.
[Google Scholar] [CrossRef] 

为你推荐