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2022 Risk-sensitive optimal stopping with unbounded terminal cost function
Damian Jelito, Łukasz Stettner
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Electron. J. Probab. 27: 1-30 (2022). DOI: 10.1214/21-EJP736


In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller–Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have multiple solutions and we give a probabilistic interpretation for the minimal and the maximal one. Also, we show how to approximate them using finite time horizon problems. The analysis, covering both discrete and continuous time case, is supported with illustrative examples.

Funding Statement

Damian Jelito and Łukasz Stettner acknowledge research support by NCN grant no. 2020/37/B/ST1/00463.


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Damian Jelito. Łukasz Stettner. "Risk-sensitive optimal stopping with unbounded terminal cost function." Electron. J. Probab. 27 1 - 30, 2022.


Received: 1 April 2021; Accepted: 16 December 2021; Published: 2022
First available in Project Euclid: 14 January 2022

Digital Object Identifier: 10.1214/21-EJP736

Primary: 49J21 , 60G40 , 93E20

Keywords: Bellman equation , dynamic programming principle , Feller-Markov process , Optimal stopping , unbounded cost function


Vol.27 • 2022
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