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A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance

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  • Angelos Dassios

    (Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • Jiwook Jang

    (Department of Actuarial Studies & Business Analytics, Macquarie Business School, Macquarie University, Sydney NSW 2109, Australia)

  • Hongbiao Zhao

    (School of Statistics and Management, Shanghai University of Finance and Economics, No. 777 Guoding Road, Shanghai 200433, China)

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

  • Angelos Dassios & Jiwook Jang & Hongbiao Zhao, 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance," Risks, MDPI, vol. 7(4), pages 1-18, October.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:4:p:103-:d:276169
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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.
    2. Luis A. Souto Arias & Pasquale Cirillo & Cornelis W. Oosterlee, 2022. "A new self-exciting jump-diffusion process for option pricing," Papers 2205.13321, arXiv.org, revised Feb 2023.

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