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The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System
Joint Authors
Ji, Shaolin
Sun, Chuanfeng
Wei, Qingmeng
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-26
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper is devoted to a stochastic differential game (SDG) of decoupled functional forward-backward stochastic differential equation (FBSDE).
For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs).
Applying the Girsanov transformation method introduced by Buckdahn and Li (2008), the upper and the lower value functions are shown to be deterministic.
We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations to the path-dependent ones.
By establishing the dynamic programming principal (DPP), we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
American Psychological Association (APA)
Ji, Shaolin& Sun, Chuanfeng& Wei, Qingmeng. 2013. The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-1032489
Modern Language Association (MLA)
Ji, Shaolin…[et al.]. The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System. Mathematical Problems in Engineering No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-1032489
American Medical Association (AMA)
Ji, Shaolin& Sun, Chuanfeng& Wei, Qingmeng. The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-1032489
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1032489