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A Partially Observed Nonzero‐Sum Stochastic Differential Game with Delays and its Application to Finance
Author(s) -
Yang Bixuan,
Guo Tiexin,
Wu Jinbiao
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1970
Subject(s) - differential game , girsanov theorem , stochastic differential equation , state variable , mathematics , mathematical economics , malliavin calculus , regular polygon , differential (mechanical device) , state (computer science) , variable (mathematics) , differential equation , mathematical optimization , stochastic partial differential equation , mathematical analysis , physics , geometry , algorithm , thermodynamics
In this paper, we deal with a new kind of partially observed nonzero‐sum differential game governed by stochastic differential delay equations. One of the special features is that the controlled system and the utility functionals involve both delays in the state variable and the control variables under different observation equations for each player. We obtain a maximum principle and a verification theorem for the game problem by virtue of Girsanov's theorem and the convex variational method. In addition, based on the theoretical results and Malliavin derivative techniques, we solve a production and consumption choice game problem.