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This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward-backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the connection an
The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the optimal control of dynamics of the McKean Vlasov type.
In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding normal vector. We also s
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakais equation. The solutions of forward backward doubly stochastic differential equations are expres
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also