Stochastic Optimal Impulse Controls with Changing Running Costs

Yuchen Cao; Jiongmin Yong

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arXiv · 2511.06628

Stochastic Optimal Impulse Controls with Changing Running Costs

Yuchen Cao·Jiongmin Yong

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Abstract

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle is to be used. The corresponding Hamilton-Jacobi-Bellman (HJB) equation (a quasi-variational inequality) is derived, which contains a parameter. The value function is a unique viscosity solution to this HJB equation by a classical argument. Further, inspired by the derivation of the Pontryagin type maximum principle for stochastic optimal controls with a non-convex control domain, we have established the maximum principle for our stochastic optimal impulse controls, allowing perturbations in optimal impulse moments.

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Yuchen Cao, Jiongmin Yong. 2025-11-10. Stochastic Optimal Impulse Controls with Changing Running Costs. https://arxiv.org/abs/2511.06628

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