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Hawkes processes in insurance: Risk model, application to empirical data and optimal investment

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  • Swishchuk, Anatoliy
  • Zagst, Rudi
  • Zeller, Gabriela

Abstract

In this paper we study a risk model with claim arrivals based on general compound Hawkes processes and show that it is suitable to model empirical insurance data. We review a law of large numbers and functional central limit theorem for this model and derive a pure diffusion approximation which allows analytical calculation of finite-time and infinite-time ruin probabilities. We use the approximation to study the influence of replacing the classical Poisson arrival process by a general compound Hawkes process on optimal investment strategies for an insurer in an incomplete market by applying results from asset–liability management.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pa:p:107-124
    DOI: 10.1016/j.insmatheco.2020.12.005
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    Cited by:

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    2. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
    3. Heidar Eyjolfsson & Dag Tj{o}stheim, 2021. "Multivariate self-exciting jump processes with applications to financial data," Papers 2108.10176, arXiv.org.
    4. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2022. "A Hawkes model with CARMA(p,q) intensity," Papers 2208.02659, arXiv.org, revised Aug 2022.

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    More about this item

    Keywords

    Hawkes process; General compound Hawkes process; Risk model; FCLT; Diffusion approximation; Optimal investment for insurers; Incomplete market;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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