Near optimality conditions in stochastic control of jump diffusion processes

Chighoub, Farid; Mezerdi, Brahim

doi:10.1016/j.sysconle.2011.07.009

Cited by 19 publications

(6 citation statements)

References 20 publications

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“…The near-optimal control problem for systems descripted by volterra integral equations has been studied by [16]. However, Chighoub et al, [8] extended Zhou's maximum principle of near-optimality to SDEs with jumps. The similar problem for systems driven by forward-backward stochastic differential equations has been solved in [5].…”

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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Section: Introductionmentioning

confidence: 99%

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

2012

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“…Since the recent work by Zhou [1], the concept of nearoptimal controls was introduced for a class of stochastic control problems. Various kinds of near-optimal stochastic control problems have been investigated in [2][3][4][5][6][7][8]. In Hafayed et al [2], the authors extended Zhou's maximum principle of near-optimality [1] to singular stochastic control.…”

Section: T) U(t))dw J (T) + G(t X Ju N (T − ) U(t) θ )N (Dθ Dt) mentioning

confidence: 99%

On mean-field stochastic maximum principle for near-optimal controls for Poisson jump diffusion with applications

Hafayed

Abba

Abbas

2013

Int. J. Dynam. Control

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In this paper, we study mean-field type stochastic control problems for systems described by mean-field stochastic differential equations with jump processes, in which the coefficients contains not only the state process but also its marginal distribution. Moreover, the cost functional is also of mean-field type. We derive necessary as well as sufficient conditions of near-optimality for our model, using Ekeland's variational principle, spike variation method and some estimates of the state and adjoint processes. Under certain concavity conditions with non-negative derivatives, we prove that the near-maximum condition on the Hamiltonian function in integral form is a sufficient condition for nearoptimality. Our result differs from the classical one in the sense that here the adjoint equation has a mean-field type, while the second-order adjoint equation remains the same as in the classical case. As an application, our results are applied to a mean-variance portfolio selection where explicit expression of the near-optimal portfolio selection strategy is obtained in the state feedback form involving both state process and its marginal distribution, via the solutions of Riccati ordinary differential equations.

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“…As a matter of fact, the near optimal control for the forward deterministic and stochastic systems have been extensively studied. We refer the reader to the monographs [4,31,33,34,35,36] for deterministic and stochastic cases. Bahlali, Khelfallah and Mezerdi [3] investigated the near optimal control of FBSDEs (see also references therein Hafayed et al [10,11,12,13,14,15]).…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, since the there are many candidates for near optimal controls, it is possible to select among them appropriates ones that are easier for analysis and implementation (see [36] reference therein).As a matter of fact, the near optimal control for the forward deterministic and stochastic systems have been extensively studied. We refer the reader to the monographs [4,31,33,34,35,36] for deterministic and stochastic cases. Bahlali, Khelfallah and Mezerdi [3] investigated the near optimal control of FBSDEs (see also references therein Hafayed et al [10,11,12,13,14,15]).…”

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confidence: 99%

Necessary condition for near optimal control of linear forward–backward stochastic differential equations

Zhang

Huang

2015

International Journal of Control

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This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex. In the previous work (Theorem 3.1) of the second and third authors [ Automatica 46 (2010) 397-404], some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it. The necessary condition of the near-optimality is established within the framework of optimality variational principle developed by Yong [SIAM J. Control Optim. 48 (2010) 4119-4156] and obtained by the convergence technique to treat the optimal control of FBSDEs in unbounded control domains by Wu [Automatica 49 (2013) 1473-1480]. Some new estimates are given here to handle the near optimality. In addition, an illustrating example is discussed as well.

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Near optimality conditions in stochastic control of jump diffusion processes

Cited by 19 publications

References 20 publications

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

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

On mean-field stochastic maximum principle for near-optimal controls for Poisson jump diffusion with applications

Necessary condition for near optimal control of linear forward–backward stochastic differential equations

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