Preprint2014

Existence of Nash Equilibrium Points for Markovian Nonzero-sum Stochastic Differential Games with Unbounded Coefficients

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Game Theory and Applications

Abstract

This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with continuous coefficient and stochastic linear growth.

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References

2005Stochastic Integration and Differential Equations 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 1998Brownian Motion and Stochastic Calculus 1960On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures 1995Zero-sum stochastic differential games and backward equations 2008Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations 2003BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations

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