Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

Menoukeu-Pamen, Olivier ORCID: 0000-0001-9306-3155 and Tangpi, Ludovic (2023) Maximum Principle for Stochastic Control of SDEs with Measurable Drifts. Journal of Optimization Theory and Applications, 197 (3). pp. 1195-1228.

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Official URL: http://dx.doi.org/10.1007/s10957-023-02209-0

Abstract

<jats:title>Abstract</jats:title><jats:p>In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in the Sobolev sense) of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the state process. Then we construct a sequence of optimal control problems with smooth coefficients by an approximation argument. Finally, we use Ekeland’s variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit. The work is notably motivated by the optimal consumption problem of investors paying wealth tax.</jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	17 Mar 2023 11:33
Last Modified:	12 Jun 2023 03:19
DOI:	10.1007/s10957-023-02209-0
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3169144