Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

Olivier Menoukeu-Pamen () and Ludovic Tangpi ()
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Olivier Menoukeu-Pamen: University of Liverpool
Ludovic Tangpi: Princeton University

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 13, 1195-1228

Abstract: 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.

Keywords: Stochastic maximum principle; Singular drifts; Sobolev differentiable flow; Ekeland’s variational principle; 60E15; 60H20; 60J60; 28C20 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-023-02209-0

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