IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i4d10.1007_s11009-022-09938-1.html
   My bibliography  Save this article

Hawkes Processes Framework With a Gamma Density As Excitation Function: Application to Natural Disasters for Insurance

Author

Listed:
  • Laurent Lesage

    (University of Lorraine, CNRS, Inria, IECL
    University of Luxembourg)

  • Madalina Deaconu

    (University of Lorraine, CNRS, Inria, IECL)

  • Antoine Lejay

    (University of Lorraine, CNRS, Inria, IECL)

  • Jorge Augusto Meira

    (University of Luxembourg)

  • Geoffrey Nichil

    (Foyer Assurances)

  • Radu State

    (University of Luxembourg)

Abstract

Hawkes processes are temporal self-exciting point processes. They are well established in earthquake modelling or finance and their application is spreading to diverse areas. Most models from the literature have two major drawbacks regarding their potential application to insurance. First, they use an exponentially-decaying form of excitation, which does not allow a delay between the occurrence of an event and its excitation effect on the process and does not fit well on insurance data consequently. Second, theoretical results developed from these models are valid only when time of observation tends to infinity, whereas the time horizon for an insurance use case is of several months or years. In this paper, we define a complete framework of Hawkes processes with a Gamma density excitation function (i.e. estimation, simulation, goodness-of-fit) instead of an exponential-decaying function and we demonstrate some mathematical properties (i.e. expectation, variance) about the transient regime of the process. We illustrate our results with real insurance data about natural disasters in Luxembourg.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09938-1
    DOI: 10.1007/s11009-022-09938-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-022-09938-1
    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/s11009-022-09938-1?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. Peter Halpin & Paul Boeck, 2013. "Modelling Dyadic Interaction with Hawkes Processes," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 793-814, October.
    2. 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.
    3. 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.
    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. Kyungsub Lee, 2024. "Discrete Hawkes process with flexible residual distribution and filtered historical simulation," Papers 2401.13890, arXiv.org.
    2. 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.

    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. 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.
    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," Post-Print hal-03040090, HAL.
    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. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2022. "Limit theorems for Hawkes processes including inhibition," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 404-426.
    6. Youngsoo Seol, 2022. "Non-Markovian Inverse Hawkes Processes," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    7. Onno Boxma & Michel Mandjes, 2021. "Shot-noise queueing models," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 121-159, October.
    8. Vipul Aggarwal & Elina H. Hwang & Yong Tan, 2021. "Learning to Be Creative: A Mutually Exciting Spatiotemporal Point Process Model for Idea Generation in Open Innovation," Information Systems Research, INFORMS, vol. 32(4), pages 1214-1235, December.
    9. Selvamuthu, Dharmaraja & Pandey, Shamiksha & Tardelli, Paola, 2023. "Limit Theorems for an extended inverse Hawkes process with general exciting functions," Statistics & Probability Letters, Elsevier, vol. 197(C).
    10. Raviar Karim & Roger J. A. Laeven & Michel Mandjes, 2021. "Exact and Asymptotic Analysis of General Multivariate Hawkes Processes and Induced Population Processes," Papers 2106.03560, arXiv.org.
    11. Li, Zhongping & Cui, Lirong & Chen, Jianhui, 2018. "Traffic accident modelling via self-exciting point processes," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 312-320.
    12. Seol, Youngsoo, 2019. "Limit theorems for an inverse Markovian Hawkes process," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    13. Li, Bo & Pang, Guodong, 2022. "Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 285-339.
    14. Youngsoo Seol, 2023. "Large Deviations for Hawkes Processes with Randomized Baseline Intensity," Mathematics, MDPI, vol. 11(8), pages 1-10, April.
    15. Andrew Daw & Jamol Pender, 2019. "On the distributions of infinite server queues with batch arrivals," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 367-401, April.
    16. Xu Sun & Yunan Liu, 2021. "Staffing many‐server queues with autoregressive inputs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 312-326, April.
    17. Luca Mucciante & Alessio Sancetta, 2023. "Estimation of an Order Book Dependent Hawkes Process for Large Datasets," Papers 2307.09077, arXiv.org.

    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:24:y:2022:i:4:d:10.1007_s11009-022-09938-1. 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.