Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
نویسندگان
چکیده
Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
منابع مشابه
Maximum Principles of Markov Regime-Switching Forward-Backward Stochastic Differential Equations with Jumps and Partial Information
Résumé/Abstract: In this talk, we present three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is developed. After, an equi...
متن کاملStochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps
متن کامل
Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
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 and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for e...
متن کاملMean-Field Backward Stochastic Volterra Integral Equations
Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...
متن کاملMaximum principle for a stochastic delayed system involving terminal state constraints
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtu...
متن کامل