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Modelling Insurance Claims During Financial Crises: A Systemic Approach

Author

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  • Francis Agana

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20 Hatfield, Pretoria 0028, South Africa
    Department of Industrial Mathematics, C.K. Tedam University of Technology and Applied Sciences, Navrongo P.O. Box 24, Ghana
    These authors contributed equally to this work.)

  • Eben Maré

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20 Hatfield, Pretoria 0028, South Africa
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce a generalised mutually exciting Hawkes process with random and independent jump intensities. This model provides a robust theoretical framework for modelling complex point processes and appropriately characterises the financial system, especially during periods of crisis. Based on this extended Hawkes process, we propose an insurance claim process and demonstrate that claim processes modelled as an aggregated process enable early detection of crises and inform optimal investment strategies in a financial system.

Suggested Citation

  • Francis Agana & Eben Maré, 2025. "Modelling Insurance Claims During Financial Crises: A Systemic Approach," JRFM, MDPI, vol. 18(6), pages 1-20, June.
    • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:6:p:307-:d:1672343
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    References listed on IDEAS

    as
    1. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.
    2. Emmanuel Bacry & Thibault Jaisson & Jean--François Muzy, 2016. "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1179-1201, August.
    3. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    4. Alan G. Hawkes, 2018. "Hawkes processes and their applications to finance: a review," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 193-198, February.
    5. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Marked Hawkes process modeling of price dynamics and volatility estimation," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 174-200.
    6. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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