IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v136y2021icp125-144.html
   My bibliography  Save this article

Risk sensitive optimal stopping

Author

Listed:
  • Jelito, Damian
  • Pitera, Marcin
  • Stettner, Łukasz

Abstract

In this paper we consider continuous time risk sensitive optimal stopping problem. Using the probabilistic approach and dyadic discrete time approximations we prove continuity of the generic optimal stopping value function for a large class of Feller-Markov processes. Also, we provide formulas for the corresponding optimal stopping policies and study regularity of approximating functions.

Suggested Citation

  • Jelito, Damian & Pitera, Marcin & Stettner, Łukasz, 2021. "Risk sensitive optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 125-144.
    • Handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:125-144
    DOI: 10.1016/j.spa.2021.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921000338
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.03.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive dyadic impulse control," Papers 1906.06389, arXiv.org.
    2. Ibtissam Hdhiri & Monia Karouf, 2011. "Risk sensitive impulse control of non-Markovian processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 1-20, August.
    3. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    4. Arapostathis, Ari & Biswas, Anup, 2018. "Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1485-1524.
    5. Damian Jelito & Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive impulse control," Papers 1912.02488, arXiv.org, revised Apr 2020.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nader Karimi & Erfan Salavati & Hirbod Assa & Hojatollah Adibi, 2023. "Sensitivity Analysis of Optimal Commodity Decision Making with Neural Networks: A Case for COVID-19," Mathematics, MDPI, vol. 11(5), pages 1-15, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Damian Jelito & Marcin Pitera & {L}ukasz Stettner, 2019. "Long-run risk sensitive impulse control," Papers 1912.02488, arXiv.org, revised Apr 2020.
    2. Pavel V. Gapeev & Peter M. Kort & Maria N. Lavrutich & Jacco J. J. Thijssen, 2022. "Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 789-813, June.
    3. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    4. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2017. "Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 487-518, June.
    5. Pavel V. Gapeev, 2022. "Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 749-788, June.
    6. Long, Mingsi & Zhang, Hongzhong, 2019. "On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2821-2849.
    7. Mr. Nikolay Aleksandrov & Mr. lajos Gyurko & Mr. Raphael A Espinoza, 2012. "Optimal Oil Production and the World Supply of Oil," IMF Working Papers 2012/294, International Monetary Fund.
    8. J. Lars Kirkby & Shi-Jie Deng, 2019. "Swing Option Pricing By Dynamic Programming With B-Spline Density Projection," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-53, December.
    9. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2013. "Optimal insurance purchase strategies via optimal multiple stopping times," Papers 1312.0424, arXiv.org.
    10. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    11. M’hamed Gaïgi & Stéphane Goutte & Idris Kharroubi & Thomas Lim, 2021. "Optimal risk management problem of natural resources: application to oil drilling," Annals of Operations Research, Springer, vol. 297(1), pages 147-166, February.
    12. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1248-1263.
    13. Christian Yeo, 2023. "An analysis of least squares regression and neural networks approximation for the pricing of swing options," Papers 2307.04510, arXiv.org.
    14. John Moriarty & Jan Palczewski, 2019. "Imbalance Market Real Options and the Valuation of Storage in Future Energy Systems," Risks, MDPI, vol. 7(2), pages 1-30, April.
    15. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.
    16. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
    17. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.
    18. Nicolas Essis-Breton & Patrice Gaillardetz, 2020. "Fast Lower and Upper Estimates for the Price of Constrained Multiple Exercise American Options by Single Pass Lookahead Search and Nearest-Neighbor Martingale," Papers 2002.11258, arXiv.org.
    19. Xianggang Lu & Lin Sun, 2023. "Discounted Risk-Sensitive Optimal Control of Switching Diffusions: Viscosity Solution and Numerical Approximation," Mathematics, MDPI, vol. 12(1), pages 1-24, December.
    20. Marie Bernhart & Huyên Pham & Peter Tankov & Xavier Warin, 2011. "Swing Options Valuation:a BSDE with Constrained Jumps Approach," Working Papers hal-00553356, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:125-144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.