On the link between infinite horizon control and quasi-stationary distributions

Nicolas Champagnat and Julien Claisse

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 771-798

Abstract: We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to study the link between infinite horizon control of these processes and an optimization problem involving their quasi-stationary distributions and the corresponding extinction rates. More precisely, we obtain an equivalent of the value function when the discount parameter is close to the threshold where the value function becomes infinite, and we characterize the optimal Markov control in this limit. To achieve this, we present a new proof of the dynamic programming principle based upon a pseudo-Markov property for controlled jump processes. We also prove the convergence to a unique quasi-stationary distribution of non-linear branching processes controlled by a Markov control conditioned on non-extinction.

Keywords: Optimal stochastic control; Infinite horizon control; Branching process; Quasi-stationary distribution; Dynamic programming (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:3:p:771-798

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DOI: 10.1016/j.spa.2018.03.018

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