A Note on Asymptotics Between Singular and Constrained Control Problems of One-Dimensional Diffusions



: Saarinen Harto, Lempa Jukka

Publisher: SPRINGER

: 2022

: Acta Applicandae Mathematicae

: ACTA APPLICANDAE MATHEMATICAE

: ACTA APPL MATH

:  13

: 181

: 1

: 17

: 0167-8019

: 1572-9036

DOI: https://doi.org/10.1007/s10440-022-00530-w

: https://link.springer.com/article/10.1007/s10440-022-00530-w

: https://research.utu.fi/converis/portal/detail/Publication/176690885


We study the asymptotic relations between certain singular and constrained control problems for one-dimensional diffusions with both discounted and ergodic objectives. In the constrained control problems the controlling is allowed only at independent Poisson arrival times. We show that when the underlying diffusion is recurrent, the solutions of the discounted problems converge in Abelian sense to those of their ergodic counterparts. Moreover, we show that the solutions of the constrained problems converge to those of their singular counterparts when the Poisson rate tends to infinity. We illustrate the results with drifted Brownian motion and Ornstein-Uhlenbeck process.

Last updated on 2024-26-11 at 18:52