Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process

Eric C.K. Cheung, Landy Rabehasaina, Jae-Kyung Woo and Ran Xu

European Journal of Operational Research, 2019, vol. 276, issue 2, 582-601

Abstract: This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted) Incurred But Not Reported claims in insurance and also the total number of customers in an infinite server queue. It is shown that the joint moments can be obtained recursively in terms of the renewal density, from which the covariance and correlation structures are derived. In particular, the fractional Poisson process defined via the renewal approach is also considered. Furthermore, the asymptotic behaviour of covariance and correlation coefficient of the aforementioned quantities is analyzed as the time horizon goes to infinity. Special attention is paid to the cases of exponential and Pareto delays. Some numerical examples in relation to our theoretical results are also presented.

Keywords: Applied probability; Fractional poisson process; Incurred But Not Reported (IBNR) claims; Infinite server queues; Correlation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:276:y:2019:i:2:p:582-601

DOI: 10.1016/j.ejor.2019.01.033

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