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Catastrophe Insurance Derivatives Pricing Using A Cox Process With Jump Diffusion Cir Intensity

Author

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  • JIWOOK JANG

    (Department of Actuarial Studies and Business Analytics, Faculty of Business and Economics, Macquarie University, Sydney NSW 2109, Australia)

  • JONG JUN PARK

    (Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea)

  • HYUN JIN JANG

    (School of Business Administration, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea)

Abstract

We propose an analytical pricing method for stop-loss reinsurance contracts and catastrophe insurance derivatives using a Cox process with jump diffusion Cox–Ingersoll–Ross (CIR) intensity. The expected payoff of these contracts is expressed by the Laplace transform of the integration of the jump diffusion CIR process and the first moment of the aggregate loss. To confirm that the proposed analytical formula provides stable and accurate insurance derivative prices, we simulate them using a full Monte Carlo method compared to those obtained from its theoretical expectation. It shows that it is much faster way to obtain them than the full Monte Carlo method. We also conduct sensitivity analysis by changing the relevant parameters in the loss intensity providing their figures.

Suggested Citation

  • Jiwook Jang & Jong Jun Park & Hyun Jin Jang, 2018. "Catastrophe Insurance Derivatives Pricing Using A Cox Process With Jump Diffusion Cir Intensity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-20, November.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:07:n:s0219024918500413
    DOI: 10.1142/S0219024918500413
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    References listed on IDEAS

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    Cited by:

    1. Park, Jong Jun & Jang, Hyun Jin & Jang, Jiwook, 2020. "Pricing arithmetic Asian options under jump diffusion CIR processes," Finance Research Letters, Elsevier, vol. 34(C).
    2. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).

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