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Analysis of Insurance Claim Settlement Process with Markovian Arrival Processes

Author

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  • Jiandong Ren

    (Department of Statistical and Actuarial Sciences, University ofWestern Ontario, London, ON N5X 0B3, Canada)

Abstract

This paper proposes a model for the claim occurrence, reporting, and handling process of insurance companies. It is assumed that insurance claims occur according to a Markovian arrival process. An incurred claim goes through some stages of a claim reporting and handling process, such as Incurred But Not Reported (IBNR), Reported But Not Settled (RBNS) and Settled (S). We derive formulas for the joint distribution and the joint moments for the amount of INBR, RBNS and Settled claims. This model generalizes previous ones in the literature, which generally assume Poisson claim arrivals. Due to the flexibility of the Markovian arrival process, the model can be used to evaluate how the claim occurring, reporting, and handling mechanisms may affect the volatilities of the amount of IBNR, RBNS and Settled claims, and the interdependencies among them.

Suggested Citation

  • Jiandong Ren, 2016. "Analysis of Insurance Claim Settlement Process with Markovian Arrival Processes," Risks, MDPI, vol. 4(1), pages 1-10, March.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:1:p:6-:d:65552
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    References listed on IDEAS

    as
    1. Hesselager, Ole, 1994. "A Markov Model for Loss Reserving," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 183-193, November.
    2. Arjas, Elja, 1989. "The Claims Reserving Problem in Non-Life Insurance: Some Structural Ideas," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 139-152, November.
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    Cited by:

    1. Hyunjoo Yoo & Bara Kim & Jeongsim Kim & Jiwook Jang, 2020. "Transform approach for discounted aggregate claims in a risk model with descendant claims," Annals of Operations Research, Springer, vol. 293(1), pages 175-192, October.

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