On Relaxed Stochastic Optimal Control for Stochastic Differential Equations Driven by G-Brownian Motion

Redjil, Amel; Choutri, Salah Eddine

doi:10.30757/alea.v15-09

Cited by 7 publications

(9 citation statements)

References 17 publications

(43 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. (i) The proof of this result is inspired by Redjil and Choutri (2018). Subtracting (3.19) from (3.20) term by term, we have…”

Section: Approximation and Existence Of Relaxed Optimal Controlmentioning

confidence: 86%

“…Then the space of strict controls must be injected into a wider space that has good properties of compactness and convexity. The set A is a compact Polish space, and P (A) be the space of probability measures on A, endowed with its Borel σ-algebra B(A), ( For more details see Redjil and Choutri (2018)).…”

Section: Problem Of G-nsfde Relaxed Controlmentioning

confidence: 99%

“…Lemma 3.6. (Redjil and Choutri (2018)) ((G-Chattering Lemma)) Let (A, d) be a separable compact metric space. Let (µ t ) t≥0 be an F P -progressively measurable process taking values in P(A).…”

Section: Approximation and Existence Of Relaxed Optimal Controlmentioning

confidence: 99%

“…Recently, Biagini et al (2018); Hu, Ji and Yang (2014); Hu and Wang (2018); Redjil and Choutri (2018) considered an optimal control problem with the uncertainty of G-Brownian motion and its quadratic variation B . In this paper we consider the following G-NFSDE…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion

Elgroud¹,

Boutabia²,

Redjil³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we study the question of existence and uniqueness of solution of neutral stochastic functional differential equations driven by G-Brownian motion (G-NSFDEs in short) on Banach space driven by relaxed controls in which the neutral term and diffusion do not depend on the control variable. By using tightness techniques and the weak convergence techniques for each probability measure in the set of all possible probabilities of our dynamic, we prove the existence of an optimal relaxed control. A motivation of are work is presented and a Numerical analysis for the uncontrolled G-NSFDE is given.

show abstract

“…Proof. (i) The proof of this result is inspired by Redjil and Choutri (2018). Subtracting (3.19) from (3.20) term by term, we have…”

Section: Approximation and Existence Of Relaxed Optimal Controlmentioning

confidence: 86%

Section: Problem Of G-nsfde Relaxed Controlmentioning

confidence: 99%

Section: Approximation and Existence Of Relaxed Optimal Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion

Elgroud¹,

Boutabia²,

Redjil³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the G-framework the existence of an optimal relaxed control is established In 2018, by Redjil and Choutri [44], where a stochastic differential equation is considered without jump term and an uncontrolled diffusion coefficient, the celebrate Chattering lemma was generalized in the G-framework and the existence of relaxed optimal control was proved. The same result in the case with jump term is recently proved by A. Redjil, H. B. Gherbal and O. Kebiri [45].…”

Section: Introductionmentioning

confidence: 99%

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Gherbal¹,

Mezerdi²

2017

AJAS

View full text Add to dashboard Cite

Abstract. This paper is concerned with optimal control of systems driven by stochastic differential equations (SDEs), with jump processes, where the control variable appears in the drift and in the jump term. We study the relaxed problem, in which admissible controls are measure-valued processes and the state variable is governed by an SDE driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, we prove that every diffusion process associated to a relaxed control is a limit of a sequence of diffusion processes associated to strict controls. As a consequence, we show that the strict and the relaxed control problems have the same value function. Using similar arguments, we prove the existence of an optimal relaxed control. In a second step, we establish a maximum principle for this type of relaxed problem.Key words: Stochastic control, Stochastic differential equation, jump process, optimal control, relaxed control -maximum principle. AMS 2010 Mathematics Subject Classification : 93E20, 60H10 Résumé (French Abstract). L'objectif de cet article est l'étude du contrôle optimal de systèmes dirigés par deséquations différentielles stochastiques (EDS), présentant des sauts, où le paramètre de contrôle apparaît aussi bien dans le drift que dans le terme de saut. Nousétudions le problème relaxé, dans lequel les contrôles admissibles sont des processusà valeurs mesures et la variable d'état est gouvernée par une EDS dirigée par une mesure de comptage appelée mesure de Poisson relaxée, dont le compensateur est une mesure produit. Sous certaines hypothèses sur les coefficients, nous montrons que tout processus de diffusion * Corresponding author Brahim Mezerdi : bmezerdi@yahoo.fr Ben Gherbal Hanane : hananebengherbal@yahoo.fr B. G. Hanane and B. Mezerdi, Afrika Statistika, Vol. 12 (2), 2017, 1287 -1312. The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps. 1288associéà un contrôle relaxé est limite d'une suite de diffusions associéesà des contrôles stricts. Comme conséquence, nousétablissons que les problèmes de contrôle strict et relaxé ont la même fonction de valeurs. En utilisant des arguments similaires, nous montrons l'existence d'un contrôle optimal relaxé. Dans une deuxièmeétape, nous démontrons un principe du maximum pour ce type de problème relaxé.

show abstract

Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps

Redjil

Gherbal

Kebiri

2021

Stochastic Analysis and Applications

View full text Add to dashboard Cite

On Relaxed Stochastic Optimal Control for Stochastic Differential Equations Driven by G-Brownian Motion

Abstract: Abstract. In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.

Cited by 7 publications

References 17 publications

Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion

Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps

Contact Info

Product

Resources

About