IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v210y2024ics0167715224000841.html
   My bibliography  Save this article

A note on series representation for the q-scale function of a class of spectrally negative Lévy processes

Author

Listed:
  • Martín-González, Ehyter M.
  • Murillo-Salas, Antonio
  • Pantí, Henry

Abstract

We provide a series representation for the q-scale function for spectrally negative Lévy processes whose jumps part has bounded variation paths. Such a series representation is in terms of completely known parameters of the associated Lévy process. We use our results to prove Doney’s conjecture in the case when the Lévy process does not have a Gaussian component.

Suggested Citation

  • Martín-González, Ehyter M. & Murillo-Salas, Antonio & Pantí, Henry, 2024. "A note on series representation for the q-scale function of a class of spectrally negative Lévy processes," Statistics & Probability Letters, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:stapro:v:210:y:2024:i:c:s0167715224000841
    DOI: 10.1016/j.spl.2024.110115
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224000841
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110115?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. David Landriault & Gordon E. Willmot, 2020. "On series expansions for scale functions and other ruin-related quantities," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(4), pages 292-306, April.
    2. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
    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. Lu, Yi & Li, Shuanming, 2009. "The Markovian regime-switching risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 296-303, April.
    2. Zhang, Aili & Li, Shuanming & Wang, Wenyuan, 2023. "A scale function based approach for solving integral-differential equations in insurance risk models," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    4. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
    5. Dickson, David C.M. & Li, Shuanming, 2010. "Finite time ruin problems for the Erlang(2) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 12-18, February.
    6. Yao, Kai & Qin, Zhongfeng, 2015. "A modified insurance risk process with uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 227-233.
    7. Li, Shuanming & Lu, Yi, 2005. "On the expected discounted penalty functions for two classes of risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 179-193, April.
    8. Kolkovska, Ekaterina T. & Martín-González, Ehyter M., 2016. "Gerber–Shiu functionals for classical risk processes perturbed by an α-stable motion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 22-28.
    9. Yang, Hu & Zhang, Zhimin, 2009. "The perturbed compound Poisson risk model with multi-layer dividend strategy," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 70-78, January.
    10. Albrecher, Hansjörg & Constantinescu, Corina & Pirsic, Gottlieb & Regensburger, Georg & Rosenkranz, Markus, 2010. "An algebraic operator approach to the analysis of Gerber-Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 42-51, February.
    11. Renata G. Alcoforado & Agnieszka I. Bergel & Rui M. R. Cardoso & Alfredo D. Egídio dos Reis & Eugenio V. Rodríguez-Martínez, 2022. "Ruin and Dividend Measures in the Renewal Dual Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 537-569, June.
    12. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2010. "An elementary approach to discrete models of dividend strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 109-116, February.
    13. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    14. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 384-397, May.
    15. Ehyter Matías Martín-González & Antonio Murillo-Salas & Henry Pantí, 2022. "Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2779-2800, December.
    16. Zhimin Zhang & Hailiang Yang & Hu Yang, 2012. "On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 973-995, December.
    17. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    18. Sendova, Kristina P. & Yang, Chen & Zhang, Ruixi, 2018. "Dividend barrier strategy: Proceed with caution," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 157-164.
    19. Lee, Wing Yan & Willmot, Gordon E., 2014. "On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 1-10.
    20. Ren, Jiandong, 2009. "A connection between the discounted and non-discounted expected penalty functions in the Sparre Andersen risk model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 324-330, February.

    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:stapro:v:210:y:2024:i:c:s0167715224000841. 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/622892/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.