2019/09/30 by Jukka Lempa, Harto Saarinen
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Applied mathematics #Computer science #Constraint (computer-aided design) #Control (management) #Control theory (sociology) #Diffusion #Diffusion process #Ergodic theory #Impulse (physics) #Impulse control #Insurance, Mortality, Demography, Risk Management #Invariant measure #Jump #Jump diffusion #Jump process #Mathematical analysis #Mathematical optimization #Mathematics #Optimal control #Physics #Poisson distribution #Singular control #Stationary ergodic process #Statistics #Stochastic processes and financial applications #demographic modeling and climate adaptation #math.OC #math.PR
paper · pdf · doi:10.1017/jpr.2020.80
published as J. Appl. Probab. 58 (2021) 1-21 · 27 pages
openalex created_date 2019/09/19 · arxiv created 2020/08/06 · openalex publication_date 2021/02/25 · arxiv updated 2021/07/01 · openalex updated_date 2026/08/05
Abstract We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.