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Forward Backward Stochastic Differential Equation Games with Delay and Noisy Memory. (arXiv:1706.09651v1 [math.OC])
来源于:arXiv
The main goal of this paper is to study a stochastic game connected to a
system of forward backward stochastic differential equations (FBSDEs) involving
delay and so-called noisy memory. We derive suffcient and necessary maximum
principles for a set of controls for the players to be a Nash equilibrium in
such a game. Furthermore, we study a corresponding FBSDE involving Malliavin
derivatives, which (to the best of our knowledge) is a kind of equation which
has not been studied before. The maximum principles give conditions for
determining the Nash equilibrium of the game. We use this to derive a closed
form Nash equilibrium for a specifc model in economics where the players aim to
maximize their consumption with respect recursive utility. 查看全文>>