A partial information non-zero sum differential game of backward stochastic differential equations with applications |
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| Authors: | Guangchen Wang Zhiyong Yu |
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| Affiliation: | 1. School of Control Science and Engineering, Shandong University, Jinan 250061, China;2. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China;3. School of Economics, Shandong University, Jinan 250100, China;1. School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China;2. Department of Mathematics, Southeast University, Nanjing 210096, China;1. School of Mathematics, Shandong University, 27 Shanda Nanlu, 250100 Jinan, PR China;2. Department of Mathematics, University of Georgia, Athens GA 30602, USA;1. International Center for Decision and Risk Analysis, School of Management, The University of Texas at Dallas, Richardson, TX, USA;2. Department of Systems Engineering and Engineering Management, College of Science and Engineering, City University of Hong Kong, Hong Kong, China;3. School of Business, The University of Technology, Sydney, NSW, Australia;4. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China;5. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China |
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| Abstract: | This paper is concerned with a new kind of non-zero sum differential game of backward stochastic differential equations (BSDEs). It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motion. We establish a necessary condition in the form of maximum principle with Pontryagin’s type for open-loop Nash equilibrium point of this type of partial information game, and then give a verification theorem which is a sufficient condition for Nash equilibrium point. The theoretical results are applied to study a partial information linear-quadratic (LQ) game and a partial information financial problem. |
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