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Ergodic control of diffusions with random intervention times

Part of: Miscellaneous topics in calculus of variations and optimal control Hamilton-Jacobi theories, including dynamic programming Markov processes

Published online by Cambridge University Press:  25 February 2021

Harto Saarinen  and
Jukka Lempa
Harto Saarinen*
Affiliation:
University of Turku
Jukka Lempa*
Affiliation:
University of Turku
*
*Postal address: Department of Mathematics and Statistics, FI - 20014 Turun Yliopisto, Finland.
*Postal address: Department of Mathematics and Statistics, FI - 20014 Turun Yliopisto, Finland.
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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.

Keywords

Bounded variation controlergodic controldiffusion processresolvent operatorPoisson processsingular stochastic control

MSC classification

Primary: 49N25: Impulsive optimal control problems
Secondary: 49L20: Dynamic programming method 60J60: Diffusion processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 1 - 21
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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