IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i2d10.1007_s11009-018-9616-5.html
   My bibliography  Save this article

Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes

Author

Listed:
  • F. Avram

    (Université de Pau et des Pays de l’Adour)

  • P. Patie

    (Cornell University)

  • J. Wang

    (Cornell University)

Abstract

The aim of this note is to provide an original proof and derive fine properties of the excessive function that characterizes the Laplace transform of the downward first hitting time to a fixed level of a non-degenerate continuous-time branching process. It hinges on a recent result by Choi and Patie (2016) on the potential theory of skip-free Markov chains and reveals, in particular, that the fundamental excessive function that characterizes the first hitting time is a purely excessive function.

Suggested Citation

  • F. Avram & P. Patie & J. Wang, 2019. "Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 391-399, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-018-9616-5
    DOI: 10.1007/s11009-018-9616-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9616-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-018-9616-5?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. Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
    2. Picard, Philippe & Lefevre, Claude, 1998. "The moments of ruin time in the classical risk model with discrete claim size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 157-172, November.
    3. Sagitov, Serik, 2017. "Tail generating functions for extendable branching processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1649-1675.
    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. Vidmar, Matija, 2023. "Complete monotonicity of time-changed Lévy processes at first passage," Statistics & Probability Letters, Elsevier, vol. 193(C).

    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. Friesen, Martin & Jin, Peng & Rüdiger, Barbara, 2020. "Existence of densities for multi-type continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5426-5452.
    2. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 374-381, December.
    3. Li, Shuanming & Garrido, José, 2002. "On the time value of ruin in the discrete time risk model," DEE - Working Papers. Business Economics. WB wb021812, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    4. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.
    5. Vaios Dermitzakis & Konstadinos Politis, 2011. "Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 749-761, December.
    6. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    7. Philipp Lukas Strietzel & Anita Behme, 2022. "Moments of the Ruin Time in a Lévy Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3075-3099, December.
    8. Möhle, Martin & Vetter, Benedict, 2023. "Scaling limits for a class of regular Ξ-coalescents," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 387-422.
    9. Le, V., 2022. "On the extinction of continuous state branching processes with competition," Statistics & Probability Letters, Elsevier, vol. 185(C).
    10. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 746-762, April.
    11. Vidmar, Matija, 2023. "Complete monotonicity of time-changed Lévy processes at first passage," Statistics & Probability Letters, Elsevier, vol. 193(C).
    12. Murillo-Salas, A. & Pérez, J.L. & Siri-Jégousse, A., 2017. "Refracted continuous-state branching processes: Self-regulating populations," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 34-44.
    13. Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
    14. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "On the moments of the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 327-350, December.
    15. Denuit, Michel, 2000. "Time stochastic s-convexity of claim processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 203-211, May.
    16. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR model with branching processes in sovereign interest rate modeling," Finance and Stochastics, Springer, vol. 21(3), pages 789-813, July.
    17. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 19-44, August.
    18. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Post-Print hal-01275397, HAL.
    19. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.
    20. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.

    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:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-018-9616-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.