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This paper studies linear quadratic (LQ) control of forward and backward stochastic difference system (FBSDS). There are two main contributions: first, the equivalent condition is obtained for the solvability of optimal control of FBSDS with multi-multiplicative noises under complete information and the analytic solution is also stated by the proposed Riccati equation. Second, the result of complete information is deduced to the situation of incomplete information, that is, the equivalent conditions of solvability and analytical solution are obtained based on Riccati equation. The main technique we use is to solve the forward–backward stochastic difference equations (FBSDEs) originated from maximum principle (MP). [ABSTRACT FROM AUTHOR]

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are common part between the follower's and the leader's information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to give the state estimate feedback representation of the Stackelberg equilibrium strategy, while its solvability is a rather difficult open problem. A special case is then studied and is applied to the continuous-time principal-agent problem. [ABSTRACT FROM AUTHOR]

This article is concerned with an optimal control problem derived by mean-field forward–backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation. The control problem is different from the existing literature concerning optimal control for mean-field stochastic systems, and has more applications in mathematical finance, e.g., asset–liability management problem with recursive utility, systematic risk model. Using a backward separation method with a decomposition technique, two optimality conditions along with two coupled forward–backward optimal filters are derived. Linear–quadratic optimal control problems for mean-field forward–backward stochastic differential equations are studied. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal control problem of backward stochastic differential delay equation under partial information. A class of time-advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. By means of ASDEs, we suggest a maximum principle of this problem and obtain necessary and sufficient conditions of optimality. We apply the theoretical results to study linear quadratic optimal control problem and obtain a forward–backward stochastic differential filtering equation (FBSDFE) with time-advanced forward equation that leads to optimal control. At the same time, some auxiliary filtering results and properties about time-advanced SDEs are also presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a new kind of non-zero sum differential game of backward stochastic differential equations (BSDEs). It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motion. We establish a necessary condition in the form of maximum principle with Pontryagin’s type for open-loop Nash equilibrium point of this type of partial information game, and then give a verification theorem which is a sufficient condition for Nash equilibrium point. The theoretical results are applied to study a partial information linear-quadratic (LQ) game and a partial information financial problem. [Copyright &y& Elsevier]

This paper is concerned with an optimal control problem driven by mean-field stochastic differential equation, where the state is partially observed via a noisy process. A new feature of the control problem is that the drift coefficient of observation equation is allowed to be a linear growth function, which immediately causes a difficulty in studying the control problem. A backward separation method with a dominated growth rate idea is used to overcome the difficulty. A maximum principle for optimality of the control problem is derived by an approximate technique. An asset–liability management problem for an insurance firm is studied. An optimal premium strategy in a feedback form is explicitly obtained. [ABSTRACT FROM AUTHOR]