Forward-backward stochastic differential equation games with delay and noisy memory. Issue 4 (3rd July 2020)

• Record Type: Journal Article
• Authors: Dahl, Kristina Rognlien
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 4(2020)
• Page Start: 708
• Page End: 729
• Publication Date: 2020-07-03
• Subjects: Forward-backward stochastic differential equations -- stochastic game -- delay -- noisy memory; 91A05 -- 91A15 -- 60H20 -- 60H10 -- 60J75 -- 34K50; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1713810
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: The goal of this paper is to study a stochastic game connected to a system of forward-backward stochastic differential equations (FBSDEs) involving delay and noisy memory. We derive sufficient and necessary maximum principles for a set of controls for the players to be a Nash equilibrium in the game. Furthermore, we study a corresponding FBSDE involving Malliavin derivatives. This kind of equation 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 an economic model where the players maximize their consumption with respect to recursive utility.