On stochastic control under Poisson observations: optimality of a barrier strategy in a general Lévy model

2022/10/02 by Kei Noba, Noba, Kei, Kazutoshi Yamazaki +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2210.00501

openalex publication_date 2022/10/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general Lévy process, we show the optimality of a periodic barrier strategy, which moves the process upward to the barrier whenever it is observed to be below it. The convergence of the optimal solutions to those in the continuous-observation case is also shown.

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