Existence and optimality conditions in stochastic control of linear BSDEs

Bahlali, Khaled; Gherbal, Boulakhras; Mezerdi, Brahim

doi:10.1515/rose.2010.010

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Then, Bahlali and al. [1] investigate a control problem, with a general cost functional by using probabilistic tools. The authors suppose that the generator is linear and assume convexity of the cost function, as well as the action space.…”

Section: Introductionmentioning

confidence: 99%

On optimal control of forward–backward stochastic differential equations

et al. 2017

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We consider a control problem where the system is driven by a decoupled as well as a coupled forwardbackward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are measure-valued processes, generalizing the usual strict controls. The proof is based on some tightness properties and weak convergence on the space D of càdlàg functions, endowed with the Jakubowsky S-topology. Moreover, under some convexity assumptions, we show that the relaxed optimal control is realized by a strict control.

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Section: Introductionmentioning

confidence: 99%

On optimal control of forward–backward stochastic differential equations

et al. 2017

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“…Actually, there has been much literature on BSDE control system driven by Brownian motion (see e.g. [2,3,5,11,10]). But to our best knowledge, there is no discussion on the optimal control problem of BSDE driven by Teugel martingales and an independent Brownian motion, which motives us to write this paper.…”

Section: Introductionmentioning

confidence: 99%

Optimal variational principle for backward stochastic control systems associated with Lévy processes

Tang

Zhang

2012

Sci. China Math.

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The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel's martingales and an independent multidimensional Brownian motion, where Teugel's martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens [14]). We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (called backward linear-quadratic problem, or BLQ problem for short) is discussed and characterized by stochastic Hamilton system.

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“…The case of an SDE where the diffusion coefficient depends explicitly on the control variable has been solved in El Karoui et al (1987);Haussmann (1986), where the optimal relaxed control is shown to be Markovian, see also Haussmann and Lepeltier (1990); Mezerdi and Bahlali (2002); Bahlali et al (2006). Existence results for systems driven by backward and forward-backward SDEs have been investigated in Bahlali et al (2010Bahlali et al ( , 2011Buckdahn et al (2010).…”

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confidence: 99%

Existence of optimal controls for systems governed by mean-field stochastic differential equations

Bahlali¹,

Mezerdi

2014

jas

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Abstract. In this paper, we study the existence of an optimal control for systems, governed by stochastic differential equations of mean-field type. For non linear systems, we prove the existence of an optimal relaxed control, by using tightness techniques and Skorokhod selection theorem. The optimal control is a measure valued process defined on another probability space. In the case where the coefficients are linear maps and the cost functions are convex, we prove by using weak convergence techniques, the existence of an optimal strict control, adapted to the initial filtration.Résumé. Dans cet article on s'intéresseà l'existence d'un contrôle optimal, pour des systèmes gouvernés par deséquations différentielles stochastiques de type champ moyen. Pour les systèmes non linéaires, on démontre un résultat d'existence d'un contrôle optimal relaxé, en utilisant des techniques de tension et le théorème de sélection de Skorokhod. Le contrôle optimal obtenu est un processusà valeurs mesures, défini sur un autre espace de probabilité. Dans le cas où les coefficients sont linéaires et les fonctions de coût sont convexes, on démontre en utilisant des techniques de convergence faible, l'existence d'un contrôle optimal strict, adaptéà la filtration initiale.

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Existence and optimality conditions in stochastic control of linear BSDEs

Cited by 4 publications

References 10 publications

On optimal control of forward–backward stochastic differential equations

On optimal control of forward–backward stochastic differential equations

Optimal variational principle for backward stochastic control systems associated with Lévy processes

Existence of optimal controls for systems governed by mean-field stochastic differential equations

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