Infinite Horizon Impulse Control of Stochastic Functional Differential Equations

Magnus Perninge

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arXiv · 2003.08833

Infinite Horizon Impulse Control of Stochastic Functional Differential Equations

Magnus Perninge

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Abstract

We consider impulse control of stochastic functional differential equations (SFDEs) driven by L\'evy processes under an additional $L^p$-Lipschitz condition on the coefficients. Our results, which are first derived for a general stochastic optimization problem over infinite horizon impulse controls and then applied to the case of a controlled SFDE, apply to the infinite horizon as well as the random horizon settings. The methodology employed to show existence of optimal controls is a probabilistic one based on the concept of Snell envelopes.

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Magnus Perninge. 2020-03-18. Infinite Horizon Impulse Control of Stochastic Functional Differential Equations. https://arxiv.org/abs/2003.08833

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