Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which linear forward-backward equation. Using decoupling technique, two Riccati obtained uniquely solvable under certain conditions. Then feedback representation control.

This paper is concerned with a stochastic linear quadratic (LQ) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two different. Closed-loop solvability established by means the corresponding Riccati equation, which implied uniform convexity cost functional. Conditions ensuring functional discussed, including issue how negative weighting matrix-valued function $R(\cdot)$ can be. Finiteness LQ problem...

A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation derived the equilibrium value function of problem. Well-posedness such an studied, and time-consistent strategies are constructed. As special cases, linear-quadratic generalized Merton's portfolio investigated.

An optimal control problem for general coupled forward-backward stochastic differential equations (FBSDEs) with mixed initial-terminal conditions is considered. The domain not assumed to be convex, and the appears in diffusion coefficient of forward equation. Necessary Pontraygin's type controls are derived by means spike variation techniques.

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the is carefully investigated. Both open-loop and closed-loop equilibrium solutions presented such kinds problems. Open-loop by means variational method decoupling forward-backward equations, which leads to a Riccati equation system lack symmetry. Closed-loop multi-person games, limit symmetric structure.

A linear-quadratic (LQ, for short) optimal control problem is consideredfor mean-field stochastic differential equations with constantcoefficients in an infinite horizon. The stabilizability of thecontrol system studied followed by the discussion thewell-posedness LQ problem. can beexpressed as a linear state feedback involving and itsmean, through solutions two algebraic Riccati equations. Thesolvability such kind investigated bymeans semi-definite programming method.

In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in drift and diffusion of the state equation. weighting matrices performance functional not assumed be definite/non-singular. existence an open-loop saddle point is characterized by adapted solution forward-backward equation with constraints, together convexity-concavity condition, closed-loop regular Riccati It turns out that there significant...

A leader-follower stochastic differential game is considered with the state equation being a linear Itô-type and cost functionals quadratic. We allow that coefficients of system those are random, controls enter diffusion equation, weight matrices for in not necessarily positive definite. The so-called open-loop strategies only. Thus, follower first solves quadratic (LQ) optimal control problem aid Riccati equation. Then leader turns to solve LQ forward-backward If such an solvable, one...

A stochastic optimal switching and impulse control problem in a finite horizon is studied. The continuity of the value function, which by no means trivial, proved. Bellman dynamic programming principle shown to be valid for such problem. Moroever, function characterized as unique viscosity solution corresponding Hamilton-Jacobi-Bellman equation.

In this paper, we obtain a global exact controllability result for class of multidimensional semilinear hyperbolic equations with superlinear nonlinearity and variable coefficients. For purpose, establish an observability estimate the linear equation unbounded potential, in which crucial constant is estimated explicitly by function norm potential. Such obtained combination pointwise Carleman differential operators analysis on regularity optimal solution to auxiliary control problem.

A time-inconsistent stochastic optimal control problem with a recursive cost functional is studied. Equilibrium strategy introduced, which time-consistent and locally approximately optimal. By means of multiperson hierarchical differential games associated partitions the time interval, family approximate equilibrium constructed, by sending mesh size interval partition to zero, an Hamilton--Jacobi--Bellman (HJB) equation derived through value function can be identified obtained. Moreover,...

Well-posedness of forward-backward stochastic differential equations (FBSDEs, for short) in $L^p$ spaces with mixed initial-terminal conditions is studied. A notion Lyapunov operator introduced, whose existence leads to a priori estimates the adapted solutions sufficient well-posedness corresponding FBSDEs, via method continuation. Various situations are discussed under which operators do exist.

This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon conditional mean-field term a switching regime environment. The orthogonal decomposition introduced [21] has been adopted. Desired algebraic Riccati equations (AREs, and system of backward differential (BSDEs, time the coefficients depending on Markov chain have derived. determination closed-loop strategy follows from solvability ARE BSDE. Moreover, BSDEs leads to...