Speaker: Olivier Menoukeu Pamen (Institute for Financial and Actuarial Mathematics (IFAM), Department of Mathematical Sciences, University of Liverpool)
Title: A Stochastic Maximum Principle for Control Problems with Irregular Drift
Abstract: This talk considers a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift coefficients. We study dynamics of the form
b(t, x,a) = b1(t, x) +b2(x)b3(t,a),
where b1 is bounded and Borel measurable, b2 is of bounded variation, and b3 is bounded and smooth. These weak regularity assumptions place the problem outside the scope of classical stochastic control theory.
We establish a Pontryagin-type stochastic maximum principle under this lowregularity framework. The analysis relies on new well-posedness and regularity results for stochastic differential equations with random drifts of bounded variation, including existence, uniqueness. A central ingredient is an explicit representation of the first variation process via integration against the space–time local time of bounded variation processes.
Our proof combines approximation methods with Ekeland’s variational principle, while a Garcia–Rodemich–Rumsey inequality provides the uniform estimates needed to control the first variation process. As an application, we derive an optimal corridor-type capital adjustment strategy for an insurance surplus model.
This talk is based on a joint work with A. M. Bogso, D. Kuissi Kamdem and R. Likibi Pellat.
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