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On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays

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  • Woo, Jae-Kyung

Abstract

In this paper, we consider an insurance portfolio containing several types of policies which may simultaneously face claims arising from the same catastrophe. A renewal counting process for the number of events causing claims and multivariate claim severities which are dependent on the occurrence time and/or the delay in reporting or payment are assumed. A unified model is proposed to study the time-dependent loss quantities such as the discounted aggregate reported/unreported claims and the number of the incurred but not reported (IBNR) claims. We then derive the joint moments of (i) different types of discounted aggregate claims until time t; and (ii) different types of discounted aggregate reported/unreported claims (including the total numbers of IBNR as special case) until time t. Finally, some numerical examples involving covariances and correlations of the aforementioned quantities are provided.

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  • Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:354-363
    DOI: 10.1016/j.insmatheco.2016.07.004
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    Cited by:

    1. Cheung, Eric C.K. & Rabehasaina, Landy & Woo, Jae-Kyung & Xu, Ran, 2019. "Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process," European Journal of Operational Research, Elsevier, vol. 276(2), pages 582-601.
    2. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.
    3. Landy Rabehasaina & Jae-Kyung Woo, 2018. "On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 307-350, December.
    4. Landy Rabehasaina & Jae-Kyung Woo, 2020. "Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 393-420, April.

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