Infinite horizon stopping problems with (nearly) total reward criteria

Jan Palczewski and Łukasz Stettner

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 3887-3920

Abstract: We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.

Keywords: Optimal stopping; Infinite horizon; Total reward; General Markovian discounting; Non-uniformly ergodic Markov processes (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:12:p:3887-3920

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DOI: 10.1016/j.spa.2014.07.009

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