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

Rui Mu; Zhen Wu

doi:10.3934/mcrf.2017010

Article Contents

2017, Volume 7, Issue 2: 289-304. Doi: 10.3934/mcrf.2017010

This issue Previous Article Minimal time synthesis for a kinematic drone model Next Article Exact controllability of linear stochastic differential equations and related problems

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

Rui Mu^1, and
Zhen Wu^2, ,

1.
Center for Financial Engineering, Soochow University, Suzhou 215006, China
2.
School of Mathematics, Shandong University, Jinan 250100, China

* Corresponding author Zhen Wu.
* Corresponding author Zhen Wu.

Revised: December 31, 2016

Published: August 2017

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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 well-posedness of the costs and the existence of a Nash equilibrium point for the game under the generalized Isaacs assumption.

Keywords:

Recursive utility,
nonzero-sum stochastic differential games,
Nash equilibrium point,
backward stochastic differential equations,
Isaacs condition.

Mathematics Subject Classification: Primary: 49N70, 60H10; Secondary: 91A15.

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References

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