Differential games of partial information forward-backward doubly SDE and applications∗
Department of Building and Real Estate, The Hong Kong Polytechnic
University, Hung Hom,
Kowloon, Hong Kong,
2 School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P.R. China
Received: 29 August 2011
Revised: 8 February 2013
This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle point of zero-sum games. To illustrate some possible applications, an example of linear-quadratic nonzero-sum differential games is worked out. Applying stochastic filtering techniques, we obtain an explicit expression of the equilibrium point.
Mathematics Subject Classification: 49N70 / 93E20 / 93E11
Key words: Stochastic differential game / partial information / forward-backward doubly stochastic differential equation / equilibrium point / stochastic filtering
This research project was funded by PolyU research accounts 1-ZV1X and G-YH96 of Hong Kong, the National Nature Science Foundation of China (11201263, 11071144, 11101242), the Nature Science Foundation of Shandong Province (ZR2012AQ004, BS2011SF010), and Independent Innovation Foundation of Shandong University (IIFSDU), China.
© EDP Sciences, SMAI, 2013