Backward-forward SDE's and stochastic differential games
type: Item
instance of: scholarly article
title: Backward-forward SDE's and stochastic differential games
zbMATH Open document ID: 0932.60065
DOI: 10.1016/S0304-4149(98)00038-6
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: The backward-forward stochastic differential equation of the form \[ X_t=x+\int_0^tf(s,X_s,Y_s,Z_s)+\int_0^t\sigma (s,X_s,Y_s,Z_s)dW_s, \] \[ Y_t=g(X_T)-\int_t^Th(s,X_s,Y_s,Z_s)-\int_t^TZ_sdW_s, \] is considered where \(W\) is a standard Brownian motion on \(\mathbb R^m\), \((X,Y,Z)\) is an adapted process with values in \(\mathbb R^m\times \mathbb R^m \times L(\mathbb R^m;\mathbb R^m)\) and \(f,h,\sigma \) and \(g\) are Lipschitz functions. Existence and uniqueness of solutions are shown under certain monotonicity assumptions. The results are applied to study the problem of existence of open-loop Nash equilibrium points of nonzero sum linear-quadratic stochastic differential games with random coefficients.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 1364497
zbMATH Keywords: backward-forward equation
zbMATH Keywords: stochastic differential game
author: Said Hamadène
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364497