Stochastic Optimal Control for Jump Diffusion Models with Singular Drifts
Abstract
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with intervention policies triggered by safety levels, notably in insurance surplus management with dividend payments and capital injections. These features place the problem outside the scope of classical stochastic maximum principle (SMP) results, which rely on global smoothness assumptions. We establish both necessary and sufficient optimality conditions for this class of control problems. Our approach combines a Sobolev-type representation of the first variation process with smooth approximations and Ekeland's variational principle. As application, we study an optimal premium adjustment and reserve management policies for an insurance whose surplus is modelled by threshold-based dividend and capital injection policies.
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BibTeX
@misc{kameh2026stochastic,
title = {{Stochastic Optimal Control for Jump Diffusion Models with Singular Drifts}},
author = {Edward Fuituh Kameh and Antoine-Marie Bogso and Olivier Menoukeu-Pamen and Felix Shu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.06176},
eprint = {2605.06176},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06176},
note = {CC0},
}
RIS
TY - UNPB
TI - Stochastic Optimal Control for Jump Diffusion Models with Singular Drifts
AU - Edward Fuituh Kameh
AU - Antoine-Marie Bogso
AU - Olivier Menoukeu-Pamen
AU - Felix Shu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2605.06176
UR - https://arxiv.org/abs/2605.06176
AB - We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with intervention policies triggered by safety levels, notably in insurance surplus management with dividend payments and capital injections. These features place the problem outside the scope of classical stochastic maximum principle (SMP) results, which rely on global smoothness assumptions. We establish both necessary and sufficient optimality conditions for this class of control problems. Our approach combines a Sobolev-type representation of the first variation process with smooth approximations and Ekeland's variational principle. As application, we study an optimal premium adjustment and reserve management policies for an insurance whose surplus is modelled by threshold-based dividend and capital injection policies.
ER -