The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients

Bahlali, Seid; Chala, Adel

doi:10.1163/1569397053300919

Cited by 6 publications

(8 citation statements)

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“…Case 1: If the coefficients f, σ , and of the underlying diffusion process and the cost functional do not explicitly depend on the expected value, Theorem 3.1 reduces to Theorem 8 proved in [4]. Case 2: If we assume G(•) ≡ K (•) ≡ 0, our necessary and sufficient conditions (Theorem 3.1, Theorem 4.1) reduce to (Theorem 3.1 and Theorem 3.3), respectively, proved in Li [17].…”

Section: Application: Singular Mean-field Linear Quadratic Control Prmentioning

confidence: 99%

“…The corresponding state process, solution of MFSDE-(1.1), is denoted by x * (•) = x u * ,η * (•). The stochastic maximum principle for singular control was considered by many authors, see for instance [2][3][4][9][10][11]13,14,16]. The first version of maximum principle for singular stochastic control problems was obtained by Cadenillas et al [9].…”

Section: Introductionmentioning

confidence: 99%

“…The first version of maximum principle for singular stochastic control problems was obtained by Cadenillas et al [9]. The first-order weak stochastic maximum principle has been studied in [4]. In [11], the authors derived stochastic maximum principle where the singular part has a linear form.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

Hafayed

2013

Commun. Math. Stat.

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This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type (MFSDEs in short), in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. The control variable has two components, the first being absolutely continuous and the second singular. We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs. These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation. The proof of our result is based on convex perturbation method of a given optimal control. The control domain is assumed to be convex. A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example. Keywords Stochastic optimal singular control • Mean-field stochastic maximum principle • Mean-field necessary and sufficient conditions of optimality • McKean-Vlasov SDEs • Convex perturbation

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Section: Application: Singular Mean-field Linear Quadratic Control Prmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

Hafayed

2013

Commun. Math. Stat.

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“…The first version of maximum principle for singular stochastic control problems was obtained by Cadenillas et al, [7]. The firstorder weak stochastic maximum principle has been studied in [3]. In [10] the authors derived stochastic maximum principle where the singular part has a linear form.…”

Section: Introductionmentioning

confidence: 99%

On necessary and sufficient conditions for near-optimal singular stochastic controls

2012

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This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland's variational principle and some dilecate estimates of the state and adjoint processes. This result is a generalization of Zhou's stochastic maximum principle for near-optimaity to singular control problem.

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“…For optimal control problem involving singular control and impulse control, the stochastic maximum principle was derived by Bahlali and Chala [15] and Dufour and Miller [16], respectively. In addition, using the dynamic programming principle, the optimal control problems involving singular control and impulse control were connected with some quasivariational inequalities by Cadenillas and Zapatero [17] and Haussmann and Suo [18], respectively.…”

Section: Introductionmentioning

confidence: 99%

Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control

2020

Adv Differ Equ

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This paper concerns a kind of stochastic optimal control problem with recursive utility described by a reflected backward stochastic differential equation (RBSDE, for short) involving diffusion type control which covers regular control problem, singular control problem and impulse control problem. To begin with, the existence and uniqueness of solution for RBSDEs involving diffusion type control is derived. Then, for the related recursive optimal control problem with obstacle constraint, a sufficient condition to obtain the optimal regular control and diffusion type control is provided. Hence, based on the connection between RBSDE and optimal stopping problem, a class of recursive optimal mixed control problem involving diffusion type control is considered to illustrate our theoretical result, and here the explicit optimal control as well as the stopping time are obtained.

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The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients

Cited by 6 publications

References 0 publications

A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control

On necessary and sufficient conditions for near-optimal singular stochastic controls

Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control

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