Forward Backward Stochastic Differential Equation Games with Delay and\n Noisy Memory

2017/06/29 by Kristina Rognlien Dahl, Dahl, Kristina Rognlien · 1 citation
Economics, Econometrics and Finance · #34K50 #60H10 #60H20 #60J75 #91A05 #91A15 #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1706.09651

openalex publication_date 2017/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main goal of this paper is to study a stochastic game connected to a\nsystem of forward backward stochastic differential equations (FBSDEs) involving\ndelay and so-called noisy memory. We derive suffcient and necessary maximum\nprinciples for a set of controls for the players to be a Nash equilibrium in\nsuch a game. Furthermore, we study a corresponding FBSDE involving Malliavin\nderivatives, which (to the best of our knowledge) is a kind of equation which\nhas not been studied before. The maximum principles give conditions for\ndetermining the Nash equilibrium of the game. We use this to derive a closed\nform Nash equilibrium for a specifc model in economics where the players aim to\nmaximize their consumption with respect recursive utility.\n

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• Stochastic Maximum Principle for Optimal Control of Anticipated Backward Stochastic Systems with Delays

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