IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i12p3887-3920.html

Infinite horizon stopping problems with (nearly) total reward criteria

Author

Listed:
  • Palczewski, Jan
  • Stettner, Łukasz

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.

Suggested Citation

  • Palczewski, Jan & Stettner, Łukasz, 2014. "Infinite horizon stopping problems with (nearly) total reward criteria," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3887-3920.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:3887-3920
    DOI: 10.1016/j.spa.2014.07.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914001653
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.07.009?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Kulik, Alexey M., 2009. "Exponential ergodicity of the solutions to SDE's with a jump noise," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 602-632, February.
    2. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    3. Wang, Jian, 2010. "Regularity of semigroups generated by Lévy type operators via coupling," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1680-1700, August.
    4. Masuda, Hiroki, 2007. "Ergodicity and exponential [beta]-mixing bounds for multidimensional diffusions with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 35-56, January.
    5. Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
    Full references (including those not matched with items on IDEAS)

    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. E. Löcherbach, 2020. "Convergence to Equilibrium for Time-Inhomogeneous Jump Diffusions with State-Dependent Jump Intensity," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2280-2314, December.
    2. Charlotte Dion & Sarah Lemler, 2020. "Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 489-515, October.
    3. Liang, Mingjie & Wang, Jian, 2020. "Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3053-3094.
    4. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    5. Teppei Ogihara & Mitja Stadje, 2024. "Efficient drift parameter estimation for ergodic solutions of backward SDEs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1181-1205, September.
    6. Stefano Pagliarani & Andrea Pascucci, 2017. "The exact Taylor formula of the implied volatility," Finance and Stochastics, Springer, vol. 21(3), pages 661-718, July.
    7. Guo, Junyu & Guo, Xiaotian & Xie, Longjie, 2021. "Quantitative stability estimates for multiscale stochastic dynamical systems," Statistics & Probability Letters, Elsevier, vol. 178(C).
    8. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    9. 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.
    10. Soren Christensen & Albrecht Irle & Stephan Jurgens, 2012. "Optimal multiple stopping with random waiting times," Papers 1205.1966, arXiv.org.
    11. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    12. Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus F. F. Schweizer & Mitja Stadje, 2020. "Robust Multiple Stopping -- A Pathwise Duality Approach," Papers 2006.01802, arXiv.org, revised Sep 2021.
    13. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    14. 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.
    15. Anatolii A. Puhalskii, 2003. "On Large Deviation Convergence of Invariant Measures," Journal of Theoretical Probability, Springer, vol. 16(3), pages 689-724, July.
    16. Liangchen Li & Michael Ludkovski, 2018. "Stochastic Switching Games," Papers 1807.03893, arXiv.org.
    17. Yuji Sakamoto & Nakahiro Yoshida, 2009. "Third-order asymptotic expansion of M-estimators for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 629-661, September.
    18. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    19. Oleksii Kulyk, 2023. "Support Theorem for Lévy-driven Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1720-1742, September.
    20. Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus Schweizer & Mitja Stadje, 2025. "Robust Multiple Stopping—A Duality Approach," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1250-1276, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:124:y:2014:i:12:p:3887-3920. 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.