JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 46-54.doi: 10.6040/j.issn.1671-9352.0.2017.483

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Forward-backward stochastic differential equations on Markov chains

XIAO Xin-ling   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, Shandong, China
  • Received:2017-09-22 Online:2018-04-20 Published:2018-04-13

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Abstract: In this paper, we mainly study the solutions about fully coupled forward-backward stochastic differential equations(FBSDE)on Markov chains. Using the usual method of continuation which is used to study fully coupled forward-backward stochastic differential equations, the Ito product rule of semimartingales, the Lebesgue control convergence theorem and iterative method, theorems about the solutions of the fully coupled forward-backward stochastic differential equations on Markov chains are obtained.

Key words: forward-backward stochastic differential equation, Markov chain, existence and uniqueness of solution

CLC Number: 

  • O211.63
[1] PARDOUX E, PENG Shige. Adapted solution of a backward stochastic differential equations [J]. System and Control Letters, 1990, 14: 55-61.
[2] COHEN S, ELLIOTT R. Solutions of backward stochastic differential equations on Markov chains [J]. Communications on Stochastic Analysis, 2008, 2(2): 251-262.
[3] COHEN S, ELLIOTT R. Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions [J]. The Annals of Applied Probability, 2010, 20(1): 267-311.
[4] COHEN S, ELLIOTT R, CHARLES E. A general comparison theorem for backward stochastic differential equations [J]. Advances in Applied Probability, 2010, 42(3): 878-898.
[5] COHEN S. Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces [J]. Stochastic Processes and their Applications, 2012, 122(4): 1601-1626.
[6] HU Ying, PENG Shige. Solutions of forward-backward stochastic differential equations [J]. Probability Theory and Related Fields, 1995, 103(2): 273-283.
[7] PENG Shige, WU Zhen. Fully coupled forward-backward stochastic differential equations [J]. SIAM Journal on Control and Optimization, 1999, 37(3):825-843.
[8] WU Zhen. Forward-backward stochastic differential equations with Brownian motion and Poisson process [J]. Acta Mathematicae Applicatae Sinica, 1999, 15(4): 433-443.
[9] JI Shaolin, LIU Haodong, XIAO Xinling. Fully coupled forward-backward stochastic differential equations on Markov chains [J]. Advances in Difference Equations, 2016, 2016(133): 1-18.
[10] IKEDA N, WATANABE S. Stochastic differential equations and diffusion processes [M]. Amsterdam:North Holland Publishing, Co, 1989.
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