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In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.
In this work we deal with the numerical solution of a
Hamilton-Jacobi-Bellman (HJB) equation with infinitely many
solutions. To compute the maximal solution – the optimal
cost of the original optimal control problem – we present a
complete discrete method based on the use of some finite elements
and penalization techniques.
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