已为您找到该学者37条结果 成果回收站
【期刊论文】A Stochastic Maximum Principle for General Mean-Field Systems
Applied Mathematics & Optimization volume,2016,74():507–534
2016年11月09日
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
无
0
-
51浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0
-
引用
【期刊论文】A Mean-field Stochastic Control Problem with Partial Observations
arXiv,2017,():
2017年02月20日
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths of the state, but also on the conditional law of the state, given the observation to date. Our problem is strongly motivated by the recent study of the mean field games and the related McKean-Vlasov stochastic control problem, but with added aspects of path-dependence and partial observation. We shall first investigate the well-posedness of the state-observation dynamics, with combined reference probability measure arguments in nonlinear filtering theory and the Schauder fixed point theorem. We then study the stochastic control problem with a partially observable system in which the conditional law appears nonlinearly in both the coefficients of the system and cost function. As a consequence the control problem is intrinsically "time-inconsistent", and we prove that the Pontryagin Stochastic Maximum Principle holds in this case and characterize the adjoint equations, which turn out to be a new form of mean-field type BSDEs.
无
0
-
37浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0
-
引用
【期刊论文】Mean-field stochastic differential equations and associated PDEs
Ann. Probab.,2017,45(2):824-878
2017年03月01日
In this paper, we consider a mean-field stochastic differential equation, also called the McKean–Vlasov equation, with initial data (t,x)∈[0,T]×Rd, whose coefficients depend on both the solution Xt,xs and its law. By considering square integrable random variables ξ as initial condition for this equation, we can easily show the flow property of the solution Xt,ξs of this new equation. Associating it with a process Xt,x,Pξs which coincides with Xt,ξs, when one substitutes ξ for x, but which has the advantage to depend on ξ only through its law Pξ, we characterize the function V(t,x,Pξ)=E[Φ(Xt,x,PξT,PXt,ξT)] under appropriate regularity conditions on the coefficients of the stochastic differential equation as the unique classical solution of a nonlocal partial differential equation of mean-field type, involving the first- and the second-order derivatives of V with respect to its space variable and the probability law. The proof bases heavily on a preliminary study of the first- and second-order derivatives of the solution of the mean-field stochastic differential equation with respect to the probability law and a corresponding Itô formula. In our approach, we use the notion of derivative with respect to a probability measure with finite second moment, introduced by Lions in [Cours au Collège de France: Théorie des jeu à champs moyens (2013)], and we extend it in a direct way to the second-order derivatives.
McKean–Vlasov equation,, Mean-field stochastic differential equation,, PDE of mean-field type,, value function
0
-
31浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0
-
引用
【期刊论文】FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE
Acta Mathematica Scientia,2006,26(3):443-450
2006年07月01日
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions.
Backward stochastic differential equations local martingale predictable representation property of martingale
0
-
26浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0
-
引用
Stochastic Processes and their Applications,2007,117(9):1234-1250
2007年09月01日
A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.
Reflected backward stochastic differential equations Comparison theorem
0
-
30浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0
-
引用
合作学者
- 暂无合作作者