2016/01/04 by Jie Xiong, Xiong, Jie, Shuaiqi Zhang +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Climate Change Policy and Economics #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1601.00538
openalex publication_date 2016/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this article, we concern a kind of partially observed non-zero sum stochastic differential game based on forward and backward stochastic differential equations (FBSDEs). It is required that each player has his own observation equation, and the corresponding open-loop Nash equilibrium control is required to adapted to the filtration that the observation process generated. To find this open-loop Nash equilibrium point, we prove the maximum principle as a necessary condition of the existence of this point, and give a verification theorem as a sufficient condition to verify it is the real open-loop Nash equilibrium point. Combined this with reality, a financial investment problem is raised. We can obtain the explicit observable investment strategy by using stochastic filtering theory and the results above.