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 study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (α), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential, we give a more...
We consider the evolution of a set according to the Huygens principle: i.e. the domain at time t>0, Λt, is the set of the points whose distance from Λ is lower than t. We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of t, and we give an algorithm to approximate the evolution. Finally we restrict...
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.