Nash equilibrium points of recursive nonzero-sum stochastic differential games with unbounded coefficients and related multiple\\ dimensional BSDEs

Abstract

This paper is concerned with recursive nonzero-sum stochastic differential game problem in Markovian framework when the drift of the state process is no longer bounded but only satisfies the linear growth condition. The costs of players are given by the initial values of related backward stochastic differential equations which, in our case, are multidimensional with continuous coefficients, whose generators are of linear growth on the volatility processes and stochastic monotonic on the value processes. We finally show the wellposedness of the costs and the existence of a Nash equilibrium point for the game under the generalized Isaacs assumption.