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L\'evy bandits under Poissonian decision times

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  • Jos'e-Luis P'erez
  • Kazutoshi Yamazaki

Abstract

We consider a version of the continuous-time multi-armed bandit problem where decision opportunities arrive at Poisson arrival times, and study its Gittins index policy. When driven by spectrally one-sided L\'evy processes, the Gittins index can be written explicitly in terms of the scale function, and is shown to converge to that in the classical L\'evy bandit of Kaspi and Mandelbaum (1995).

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  • Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2023. "L\'evy bandits under Poissonian decision times," Papers 2301.07798, arXiv.org.
    • Handle: RePEc:arx:papers:2301.07798
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    References listed on IDEAS

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    1. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    2. Zhao, Yongxia & Chen, Ping & Yang, Hailiang, 2017. "Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 135-146.
    3. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    4. Irmina Czarna & Zbigniew Palmowski, 2014. "Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 239-256, April.
    5. José-Luis Pérez & Kazutoshi Yamazaki, 2018. "Mixed Periodic-Classical Barrier Strategies for Lévy Risk Processes," Risks, MDPI, vol. 6(2), pages 1-39, April.
    6. Zbigniew Palmowski & José Luis Pérez & Kazutoshi Yamazaki, 2021. "Double continuation regions for American options under Poisson exercise opportunities," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 722-771, April.
    7. Jos'e-Luis P'erez & Kazutoshi Yamazaki & Alain Bensoussan, 2018. "Optimal periodic replenishment policies for spectrally positive L\'evy demand processes," Papers 1806.09216, arXiv.org, revised Sep 2020.
    8. Zbigniew Palmowski & Jos'e Luis P'erez & Budhi Arta Surya & Kazutoshi Yamazaki, 2019. "The Leland-Toft optimal capital structure model under Poisson observations," Papers 1904.03356, arXiv.org, revised Mar 2020.
    9. Zbigniew Palmowski & José Luis Pérez & Budhi Arta Surya & Kazutoshi Yamazaki, 2020. "The Leland–Toft optimal capital structure model under Poisson observations," Finance and Stochastics, Springer, vol. 24(4), pages 1035-1082, October.
    10. A. Kyprianou & B. Surya, 2007. "Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels," Finance and Stochastics, Springer, vol. 11(1), pages 131-152, January.
    11. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.
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