IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i2d10.1007_s11009-019-09722-8.html
   My bibliography  Save this article

Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims

Author

Listed:
  • Zailei Cheng

    (Florida State University)

  • Youngsoo Seol

    (Dong-A University)

Abstract

We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article is to establish a diffusion approximation by verifying a functional central limit theorem and to compute the ruin probability in finite-time horizon. Numerical results will also be given.

Suggested Citation

  • Zailei Cheng & Youngsoo Seol, 2020. "Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 555-571, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09722-8
    DOI: 10.1007/s11009-019-09722-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09722-8
    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/s11009-019-09722-8?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. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. Harrison, J. Michael, 1977. "Ruin problems with compounding assets," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 67-79, February.
    3. Gabriele Stabile & Giovanni Luca Torrisi, 2010. "Risk Processes with Non-stationary Hawkes Claims Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 415-429, September.
    4. Gusto Gaelle & Schbath Sophie, 2005. "FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-28, September.
    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. Laurent Lesage & Madalina Deaconu & Antoine Lejay & Jorge Augusto Meira & Geoffrey Nichil & Radu State, 2022. "Hawkes processes framework with a Gamma density as excitation function: application to natural disasters for insurance," Post-Print hal-03040090, HAL.
    2. Laurent Lesage & Madalina Deaconu & Antoine Lejay & Jorge Augusto Meira & Geoffrey Nichil & Radu State, 2022. "Hawkes Processes Framework With a Gamma Density As Excitation Function: Application to Natural Disasters for Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2509-2537, December.
    3. Wang, Haixu, 2022. "Limit theorems for a discrete-time marked Hawkes process," Statistics & Probability Letters, Elsevier, vol. 184(C).
    4. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    5. Laurent Lesage & Madalina Deaconu & Antoine Lejay & Jorge Augusto Meira & Geoffrey Nichil & Radu State, 2020. "Hawkes processes framework with a Gamma density as excitation function: application to natural disasters for insurance," Working Papers hal-03040090, HAL.

    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. Zailei Cheng & Youngsoo Seol, 2018. "Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Papers 1801.07595, arXiv.org, revised Aug 2019.
    2. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    3. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    4. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
    5. Cao, Jingyi & Landriault, David & Li, Bin, 2020. "Optimal reinsurance-investment strategy for a dynamic contagion claim model," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 206-215.
    6. Ulrich Horst & Wei Xu, 2019. "Functional Limit Theorems for Marked Hawkes Point Measures ," Working Papers hal-02443841, HAL.
    7. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    8. Horst, Ulrich & Xu, Wei, 2021. "Functional limit theorems for marked Hawkes point measures," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 94-131.
    9. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    10. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.
    11. Peng Wu & Marcello Rambaldi & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2019. "Queue-reactive Hawkes models for the order flow," Papers 1901.08938, arXiv.org.
    12. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    13. Yuen, Kam C. & Wang, Guojing & Ng, Kai W., 2004. "Ruin probabilities for a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 259-274, April.
    14. Kostadinova, Radostina, 2007. "Optimal investment for insurers when the stock price follows an exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 250-263, September.
    15. Braunsteins, Peter & Mandjes, Michel, 2023. "The Cramér-Lundberg model with a fluctuating number of clients," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 1-22.
    16. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    17. Ulrich Horst & Wei Xu, 2024. "Functional Limit Theorems for Hawkes Processes," Papers 2401.11495, arXiv.org, revised Dec 2024.
    18. Kyungsub Lee, 2024. "Discrete Hawkes process with flexible residual distribution and filtered historical simulation," Papers 2401.13890, arXiv.org.
    19. Lucio Maria Calcagnile & Giacomo Bormetti & Michele Treccani & Stefano Marmi & Fabrizio Lillo, 2015. "Collective synchronization and high frequency systemic instabilities in financial markets," Papers 1505.00704, arXiv.org.
    20. Xiaofei Lu & Frédéric Abergel, 2017. "Limit order book modelling with high dimensional Hawkes processes," Working Papers hal-01512430, 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:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09722-8. 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.