Maximum Principles for Forward-Backward Stochastic Control Systems with Correlated State and Observation Noises

Wang, Guangchen; Wu, Zhen; Xiong, Jie

doi:10.1137/110846920

Cited by 96 publications

(92 citation statements)

References 26 publications

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“…However, it excludes some important applications. Very recently, Wang, Wu and Xiong [18] improved Problem (NLC). They assumed that h grows linearly with respect to x, but the diffusion coefficient σ is uniformly bounded in (t, x, v); moreover, the set of admissible controls is…”

mentioning

confidence: 99%

“…With the assumptions and smooth conditions about coefficients, Lemma 3.2 in [18] proved that the Radon Nikodym derivative λ v t satisfies lE(λ v t ) p < +∞, 0 ≤ t ≤ T, for a p > 1. Combining high-order moment estimates of adjoint processes of (x, y, z, λ) with an approximation method by bounded and smooth functions, a necessary condition for optimality was established.…”

mentioning

confidence: 99%

“…Because the cross-variation of x v t and Y v t is t 0 c s h s ds, and the drift coefficient of the observation equation is linear with respect to the state x, the LQ problem is different from the setups of [1], [2], [30], [31], [15], [22], [17], [14], [23], [18] and the references therein. In addition, it seems that the approximation method with Girsanov's transformation introduced in [18] is not available to deal with the LQ problem. One possible reason is as follows.…”

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confidence: 99%

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A Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic Differential Equations With Partial Information

Wang

Xiong

2015

IEEE Trans. Automat. Contr.

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This paper studies a linear-quadratic optimal control problem derived by forward-backward stochastic differential equations, where the drift coefficient of the observation equation is linear with respect to the state x, and the observation noise is correlated with the state noise, in the sense that the cross-variation of the state and the observation is nonzero. A backward separation approach is introduced. Combining it with variational method and stochastic filtering, two optimality conditions and a feedback representation of optimal control are derived. Closed-form optimal solutions are obtained in some particular cases. As an application of the optimality conditions, a generalized recursive utility problem from financial markets is solved explicitly.Index terms-Linear-quadratic optimal control, forwardbackward stochastic differential equation, partial information, correlated state and observation noises, closed-form solution, recursive utility.

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confidence: 99%

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confidence: 99%

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confidence: 99%

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A Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic Differential Equations With Partial Information

Wang

Xiong

2015

IEEE Trans. Automat. Contr.

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“…is a solution of (22). Therefore, the result follows by the existence and uniqueness of the solutionȂ(t, 0, ) of (22) withȂ(0, 0, ) = 0.…”

Section: Proof Using the Itô Formula To G(0 T)∫ T 0 C(s) G(0s)mentioning

confidence: 75%

“…whereȂ(t, , 0) satisfies the SDE (21) andȂ(t, 0, ) satisfies the stochastic impulse equation (22). Since (t) ∈   is independent of (t) ∈   for 0 ≤ t ≤ T, (27) holds for all ( , ) ∈   if and only if…”

Section: Theorem 1 (Maximum Principle)mentioning

confidence: 99%

A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward‐backward systems

Wang¹,

Song²,

Feng³

2015

Asian Journal of Control

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We consider a combined stochastic control and impulse control problem of forward-backward systems driven by Lévy processes, where both the system coefficients and the objective performance functional are allowed to be random, non-Markovian; the information available to the controller is partial information. Applying a Malliavin calculus approach, we derive a maximum principle for this control problem, where the adjoint processes are explicitly represented by the parameters and the states of the system. Finally, we give two examples of applications.

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Linear‐Quadratic Optimal Control Problem for Partially Observed Forward‐Backward Stochastic Differential Equations of Mean‐Field Type

Liu

2016

Asian Journal of Control

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This paper is concerned with the linear-quadratic optimal control problem for partially observed forward-backward stochastic differential equations (FBSDEs) of mean-field type. Based on the classical spike variational method, backward separation approach as well as filtering technique, we first derive the necessary and sufficient conditions of the optimal control problem with the non-convex domain. Nextly, by means of the decoupling technique, we obtain two Riccati equations, which are uniquely solvable under certain conditions. Also, the optimal cost functional is represented by the solutions of the Riccati equations for the special case.

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Maximum Principles for Forward-Backward Stochastic Control Systems with Correlated State and Observation Noises

Cited by 96 publications

References 26 publications

A Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic Differential Equations With Partial Information

A Linear-Quadratic Optimal Control Problem of Forward-Backward Stochastic Differential Equations With Partial Information

A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward‐backward systems

Linear‐Quadratic Optimal Control Problem for Partially Observed Forward‐Backward Stochastic Differential Equations of Mean‐Field Type

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