Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

Olivier Menoukeu-Pamen, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageAmerican English
Pages (from-to)1195-1228
Number of pages34
JournalJournal of Optimization Theory and Applications
Volume197
Issue number3
DOIs
StatePublished - Jun 2023

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research

Keywords

  • Ekeland’s variational principle
  • Singular drifts
  • Sobolev differentiable flow
  • Stochastic maximum principle

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