Abstract
The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ma Jin, Protter P, Yong, Jiongmin. Solving forward-backward stochastic differential equations explicitly—a four step scheme[J].Probab Theory Related Fields, 1994,98(2):339–359.
Hu Ying, Peng Shige. Solution of forward-backard stochastic differential equations[J].Probab Theory Related Fields, 1995,103(2):273–283.
Peng Shige Wu Zhen. Fully coupled forward-backward stochastic differential equations and applications to optimal control[J].SIAM J Control Optim, 1999,37(3):825–843.
Yong Jiongmin. Finding adapted solution of forward-backward stochastic differential equations-method of continuation[J].Probab Theory Related Fields, 1997,107(3):537–572.
Tang Shanjian, Li Xunjing. Necessary condition for optimal control of stochastic systems with random jumps[J].SIAM J Control Optim, 1994,32(5):1447–1475.
Situ Rong. On solution of backward stochastic differential equations with jumps and applications[J].Stochastic Processes and Their Applications, 1997,66(2):209–236.
Wu Zhen. Forward-backward stochastic differential equations with Brownian motion and Poisson process[J].Acta Mathematicae Applicatae Sinica, 1999,15(3):433–443.
Friedman A.Differential Games[M]. Wiley-Interscience, New York, 1971.
Bensoussan A. Point de Nash dans de cas de fonctionnelles quadratiques et jeux différentiels àN personnes[J].SIAM J Control Optim, 1974,12(3):728–742.
Eisele T. Nonexistence and nonuniqueness of open-loop equilibria in linear-quadratic differential games[J].J Math Anal Appl, 1982,37(3):443–468.
Hamadène S. Nonzero sum linear-quadratic stochastic differential games and backward-forward equations[J].Stochastic Anal Appl, 1999,17(2):117–130.
Ikeda N, Watanabe S.Stochastic Differential Equations and Diffusion Processes[M]. North-Holland, Kodansha, 1981.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Lin, Zong-chi, Original Member of Editorial Committee, AMM)
Project supported by the National Natural Science Foundation, of China (No. 10371067); the Planne Item for the Outstanding Young Teachers of Ministry of Ministry of Education of China (No. 2057); the Special Fund for Ph. D. Program of Ministry of Education of China (No. 20020422020) and the Fok Ying Tung Education Foundation for Young College Teachers (No. 91064).
Rights and permissions
About this article
Cite this article
Zhen, W., Zhi-yong, W. Linear quadratic nonzero-sum differential games with random jumps. Appl Math Mech 26, 1034–1039 (2005). https://doi.org/10.1007/BF02466416
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02466416