Optimal stopping of the stable process with state-dependent killing

KEES Van Schaik; Alexander R. Watson; Xin Xu

doi:10.3150/24-BEJ1741

Optimal stopping of the stable process with state-dependent killing

KEES Van Schaik, Alexander R. Watson, Xin Xu

Department of Financial and Actuarial Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the solution of an optimal stopping problem for a stable Lévy process killed at state-dependent rate. The killing rate is chosen in such a way that the killed process remains self-similar, and the solution to the optimal stopping problem is obtained by characterising a self-similar Markov process associated with the stable process. The optimal stopping strategy is to stop upon first passage into an interval, found explicitly in terms of the parameters of the model.

Original language	English
Pages (from-to)	609-629
Number of pages	21
Journal	Bernoulli
Volume	31
Issue number	1
DOIs	https://doi.org/10.3150/24-BEJ1741
Publication status	Published - Feb 2025

Keywords

Lamperti transformation
Lévy process
Markov additive process
omega-clock
optimal stopping
self-similar Markov process
stable process

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10.3150/24-BEJ1741

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abstract = "We describe the solution of an optimal stopping problem for a stable L{\'e}vy process killed at state-dependent rate. The killing rate is chosen in such a way that the killed process remains self-similar, and the solution to the optimal stopping problem is obtained by characterising a self-similar Markov process associated with the stable process. The optimal stopping strategy is to stop upon first passage into an interval, found explicitly in terms of the parameters of the model.",

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AB - We describe the solution of an optimal stopping problem for a stable Lévy process killed at state-dependent rate. The killing rate is chosen in such a way that the killed process remains self-similar, and the solution to the optimal stopping problem is obtained by characterising a self-similar Markov process associated with the stable process. The optimal stopping strategy is to stop upon first passage into an interval, found explicitly in terms of the parameters of the model.

KW - Lamperti transformation

KW - Lévy process

KW - Markov additive process

KW - omega-clock

KW - optimal stopping

KW - self-similar Markov process

KW - stable process

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JO - Bernoulli

JF - Bernoulli

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ER -

Optimal stopping of the stable process with state-dependent killing

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Keywords

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