A variational formula for nonzero-sum stochastic differential games of FBSDEs and applications
type: Item
instance of: scholarly article
title: A variational formula for nonzero-sum stochastic differential games of FBSDEs and applications
zbMATH Open document ID: 1407.49059
DOI: 10.1155/2014/283418
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: A nonzero-sum stochastic differential game problem is investigated for fully coupled forward-backward stochastic differential equations (FBSDEs in short) where the control domain is not necessarily convex. A variational formula for the cost functional in a given spike perturbation direction of control processes is derived by the Hamiltonian and associated adjoint systems. As an application, a global stochastic maximum principle of Pontryagin's type for open-loop Nash equilibrium points is established. Finally, an example of a linear quadratic nonzero-sum game problem is presented to illustrate that the theories may have interesting practical applications and the corresponding Nash equilibrium point is characterized by the optimality system. Here the optimality system is a fully coupled FBSDE with double dimensions (DFBSDEs in short) which consists of the state equation, the adjoint equation, and the optimality conditions.
Mathematics Subject Classification ID: 49N70
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 7016067
Wikidata QID: Q59065404
author: Mao-ning Tang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/283418
OpenAlex ID: W2050584239
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description: scientific article; zbMATH DE number 7016067