Near optimality conditions in stochastic control of jump diffusion processes

Farid Chighoub; Brahim Mezerdi

doi:10.1016/j.sysconle.2011.07.009

Near optimality conditions in stochastic control of jump diffusion processes

Farid Chighoub, Brahim Mezerdi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland's variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly.

Original language	English
Pages (from-to)	907-916
Number of pages	10
Journal	Systems and Control Letters
Volume	60
Issue number	11
DOIs	https://doi.org/10.1016/j.sysconle.2011.07.009
State	Published - Nov 2011
Externally published	Yes

Keywords

Adjoint process
Diffusion with jumps
Maximum principle
Near-optimal control

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/j.sysconle.2011.07.009

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abstract = "This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland's variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly.",

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AB - This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland's variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly.

KW - Adjoint process

KW - Diffusion with jumps

KW - Maximum principle

KW - Near-optimal control

UR - https://www.scopus.com/pages/publications/80053379326

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M3 - Article

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JF - Systems and Control Letters

IS - 11

ER -

Near optimality conditions in stochastic control of jump diffusion processes

Abstract

Keywords

ASJC Scopus subject areas

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