Existence of relaxed stochastic optimal control for <i>G</i>-SDEs with controlled jumps

Redjil, Amel; Gherbal, Hanane Ben; Kebiri, Omar

doi:10.1080/07362994.2021.1991809

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…These results have been extended to mean-field systems in [3][4][5]. See also [2,12,32] for versions of the relaxed stochastic maximum principle including doubly forward-backward stochastic differential equations and stochastic equations driven by G-Brownian motion.…”

Section: The Relaxed Stochastic Maximum Principle and Contributions O...mentioning

confidence: 99%

On the maximum principle for relaxed control problems of nonlinear stochastic systems

Mezerdi,

Mezerdi

2024

Adv Cont Discr Mod

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We consider optimal control problems for a system governed by a stochastic differential equation driven by a d-dimensional Brownian motion where both the drift and the diffusion coefficient are controlled. It is well known that without additional convexity conditions the strict control problem does not admit an optimal control. To overcome this difficulty, we consider the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is governed by a stochastic differential equation driven by a continuous orthogonal martingale measure. This relaxed model admits an optimal control that can be approximated by a sequence of strict controls by the so-called chattering lemma. We establish optimality necessary conditions, in terms of two adjoint processes, extending Peng’s maximum principle to relaxed control problems. We show that relaxing the drift and diffusion martingale parts directly as in deterministic control does not lead to a true relaxed model as the obtained controlled dynamics is not continuous in the control variable.

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Section: The Relaxed Stochastic Maximum Principle and Contributions O...mentioning

confidence: 99%

On the maximum principle for relaxed control problems of nonlinear stochastic systems

Mezerdi,

Mezerdi

2024

Adv Cont Discr Mod

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“…This theory developed quickly due to the great interest of many researchers, which led to the publication of many articles investigating stochastic differential equations driven by G-Brownian motion (G-SDEs) and their applications (see e.g. [6,8,9,12,14,23,24,25] and the references therein). Also, a few works concerned with their qualitative properties (see, for instance [7,16,17]).…”

Section: Introductionmentioning

confidence: 99%

Temporal regularity of stochastic differential equations driven by G-Brownian motion

Redjil,

Arab,

Ben Gherbal

et al. 2024

Stat., optim. inf. comput.

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On solvability and optimal controls for impulsive stochastic integrodifferential varying-coefficient model

Chalishajar,

K.,

et al. 2024

Automatika

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

Cited by 5 publications

References 27 publications

On the maximum principle for relaxed control problems of nonlinear stochastic systems

On the maximum principle for relaxed control problems of nonlinear stochastic systems

Temporal regularity of stochastic differential equations driven by G-Brownian motion

On solvability and optimal controls for impulsive stochastic integrodifferential varying-coefficient model

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