Controlled Filtered Poisson Processes

Mario Lefebvre ()
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Mario Lefebvre: Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC H3C 3A7, Canada

Mathematics, 2025, vol. 13, issue 2, 1-12

Abstract: Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming equation satisfied by the value function is derived. To obtain the value function, and hence the optimal control, a non-linear integro-differential equation must be solved, subject to the appropriate boundary conditions. Various cases for the size of the jumps are treated and explicit results are obtained.

Keywords: stochastic control; dynamic programming; homing problem; first-passage time; integro-differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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