Ergodic control of diffusions with random intervention times

: Saarinen Harto, Lempa Jukka

Publisher: CAMBRIDGE UNIV PRESS

: 2021

: Journal of Applied Probability

: JOURNAL OF APPLIED PROBABILITY

: J APPL PROBAB

: PII S0021900220000807

: 58

: 1

: 21

: 0021-9002

: 1475-6072

DOI: https://doi.org/10.1017/jpr.2020.80

: https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/ergodic-control-of-diffusions-with-random-intervention-times/3D9F3F2E263C50FEDB8DB94FBA5565C7

: https://research.utu.fi/converis/portal/detail/Publication/53665205

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.

ergodic-control-of-diffusions-with-random-intervention-times.pdf