Infinite Horizon Impulse Control of Stochastic Functional Differential Equations

2020/03/18 by Magnus Perninge, Perninge, Magnus
Economics, Econometrics and Finance · #49L20 #60G40 #62P30 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2003.08833

openalex publication_date 2020/03/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We consider impulse control of stochastic functional differential equations (SFDEs) driven by Lévy 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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