Existence and uniqueness results of fully coupled forward-backward stochastic differential equations with an arbitrarily large time duration are obtained. Some Hamilton systems arising in optimal control mathematical finance can be treated within our framework.

In this paper, we study the well-posedness of Forward–Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find unified scheme which combines all existing methodology literature, and address some fundamental longstanding problems for FBSDEs. An important device decoupling random field that regular (uniformly Lipschitz its spatial variable). We show regulariy such closely related bounded solution an associated characteristic BSDE,...

In this paper, we study a partial information optimal control problem derived by forward-backward stochastic systems with correlated noises between the system and observation. Utilizing direct method, an approximation Malliavin derivative establish three versions of maximum principle (i.e., necessary condition) for control. To show their applications, work out two illustrative examples within frameworks linear-quadratic recursive utility then solve them via principles filtering.

This paper studies a linear-quadratic optimal control problem derived by forward-backward stochastic differential equations, where the drift coefficient of observation equation is linear with respect to state $x$, and noise correlated noise, in sense that cross-variation nonzero. A backward separation approach introduced. Combining it variational method filtering, two optimality conditions feedback representation are derived. Closed-form solutions obtained some particular cases. As an...

This paper introduces the backward mean-field (MF) linear-quadratic-Gaussian (LQG) games (for short, BMFLQG) of weakly coupled stochastic large-population system. In contrast to well-studied forward LQG games, individual state in our system follows differential equation (BSDE) whose terminal instead initial condition should be prescribed. Two classes BMFLQG are discussed here and their decentralized strategies derived through consistency condition. first class, agents dynamics full...

We investigate the optimal control problems for backward doubly stochastic systems. As a necessary condition of we obtain maximum principle. found that deduced Hamiltonian system exactly corresponds to type time-symmetric forward-backward differential equations, which was first introduced by Peng and Shi [C. R. Math. Acad. Sci. Paris, 336 (2003), pp. 773–778]. Applying principle linear quadratic problems, unique control. The existence uniqueness solution is also obtained generalized...

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraint for cost functional described by solution a reflected backward differential equation. We give dynamic programming principle and show that value function is unique viscosity corresponding Hamilton–Jacobi–Bellman

This paper investigates the stabilization and control problems for linear continuous-time mean-field systems. Under standard assumptions, necessary sufficient conditions to stabilize systems in mean-square sense are explored first time. It is shown that, under assumption of exact detectability (exact observability), system stabilizable if only a coupled algebraic Riccati equation admits unique positive-semidefinite solution (positive-definite solution), which coincides with classical results...

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and variables. This will lead to kind of generalized forward‐backward differential equations (FBSDEs) Itô’s as forward anticipated backward equations. Especially, we present the feedback regulator time via new type Riccati also apply population problem.

We consider a stochastic optimal control problem of forward-backward system in which the variable consists two components: continuous and impulse control. The domain is assumed to be convex. Necessary optimality conditions Pontryagin maximum principle type are obtained for this problem. also give additional conditions, under necessary turn out sufficient.

This paper is concerned with a new kind of Stackelberg differential game mean‐field backward stochastic equations (MF‐BSDEs). By means four Riccati (REs), the follower first solves LQ optimal control problem and gets corresponding open‐loop feedback representation. Then leader turns to solve an optimization for 1 × 2 forward‐backward system. In virtue some high‐dimensional complicated REs, we obtain equilibrium, it admits state Finally, as applications, class pension fund problems which can...

<p style='text-indent:20px;'>This paper is first concerned with one kind of discrete-time stochastic optimal control problem convex domains, for which necessary condition in the form Pontryagin's maximum principle and sufficient optimality are derived. The results then extended to two kinds games. Two illustrative examples studied, explicit strategies given. This establishes a rigorous version clear concise way paves road further related topics.</p>

Based on FreeStyle Libre, we designed QT AIR, an advanced real-time, calibrated Continuous Glucose Monitoring (CGM) device. This study aim to validate the consistency and clinical accuracy of product by comparing capillary blood glucose (CBG) with CGM data in both in-hospital outpatient scenarios. Results devices were compared random values from users settings. The CGMs was assessed through analysis, Bland-Altman calculation MARD MAD, Consensus Error Grids, as well analysis using Deviation...