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On a risk model with claim investigation

Author

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  • Huynh, Mirabelle
  • Landriault, David
  • Shi, Tianxiang
  • Willmot, Gordon E.

Abstract

In this paper, a queue-based claims investigation mechanism is considered to model an insurer’s claim processing practices. The resulting risk model may be viewed as a first step in developing models with more realistic claim investigation mechanisms. Related to claim investigations, claim settlement delays and time dependent payments have been studied in a ruin context by, e.g. Taylor (1979), Cai and Dickson (2002), and Trufin et al. (2011). However, little has been done on queue-based investigation mechanisms. We first demonstrate the impact of a particular claim investigation system on some common ruin-related quantities when claims arrive according to a compound Poisson process, and investigation times are of a combination of exponential form. Probabilistic interpretations for the defective renewal equation components are also provided. Finally, via numerical examples, we explore various risk management questions related to this problem such as how claim investigation strategies can help an insurer control its activities within its risk appetite.

Suggested Citation

  • Huynh, Mirabelle & Landriault, David & Shi, Tianxiang & Willmot, Gordon E., 2015. "On a risk model with claim investigation," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 37-45.
  • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:37-45
    DOI: 10.1016/j.insmatheco.2015.08.010
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    References listed on IDEAS

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    1. Landriault, David & Willmot, Gordon E. & Xu, Di, 2014. "On the analysis of time dependent claims in a class of birth process claim count models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 168-173.
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    7. Taylor, G. C., 1979. "Probability of Ruin under Inflationary Conditions or under Experience Rating," ASTIN Bulletin, Cambridge University Press, vol. 10(2), pages 149-162, March.
    8. Trufin, Julien & Albrecher, Hansjorg & Denuit, Michel, 2011. "Ruin problems under IBNR dynamics," LIDAM Reprints ISBA 2011045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. David Landriault & Gordon Willmot, 2009. "On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 252-270.
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    Cited by:

    1. Ahn, Soohan & Badescu, Andrei L. & Cheung, Eric C.K. & Kim, Jeong-Rae, 2018. "An IBNR–RBNS insurance risk model with marked Poisson arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 26-42.

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