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A generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance

Author

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  • Dassios, Angelos
  • Jang, Jiwook
  • Zhao, Hongbiao
Abstract
In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the literature with self-exciting and external-exciting jumps. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.

Suggested Citation

  • Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2019. "A generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance," LSE Research Online Documents on Economics 102043, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:102043
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    File URL: http://eprints.lse.ac.uk/102043/
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    References listed on IDEAS

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    1. Kira Henshaw & Corina Constantinescu & Olivier Menoukeu Pamen, 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives," Risks, MDPI, vol. 8(1), pages 1-28, February.

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    More about this item

    Keywords

    contagion risk; insurance premium; aggregate claims; default-free bond pricing; self-exciting process; Hawkes process; CIR process;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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