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Forward-backward stochastic differential equation games with delay and noisy memory

Stochastic analysis and applications, 2020-07, Vol.38 (4), p.708-729 [Peer Reviewed Journal]

2020 The Author(s). Published with license by Taylor and Francis Group, LLC 2020 ;info:eu-repo/semantics/openAccess ;ISSN: 0736-2994 ;EISSN: 1532-9356 ;DOI: 10.1080/07362994.2020.1713810

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  • Title:
    Forward-backward stochastic differential equation games with delay and noisy memory
  • Author: Dahl, Kristina Rognlien
  • Subjects: delay ; Forward-backward stochastic differential equations ; noisy memory ; stochastic game
  • Is Part Of: Stochastic analysis and applications, 2020-07, Vol.38 (4), p.708-729
  • Description: 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.
  • Publisher: Taylor & Francis
  • Language: English;Norwegian
  • Identifier: ISSN: 0736-2994
    EISSN: 1532-9356
    DOI: 10.1080/07362994.2020.1713810
  • Source: Taylor & Francis Open Access
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