an:07034947
Zbl 1430.90188
Cheung, Eric C. K.; Rabehasaina, Landy; Woo, Jae-Kyung; Xu, Ran
Asymptotic correlation structure of discounted incurred but not reported claims under fractional Poisson arrival process
EN
Eur. J. Oper. Res. 276, No. 2, 582-601 (2019).
00429495
2019
j
90B22 60K10 60G22
applied probability; fractional Poisson process; incurred but not reported (IBNR) claims; infinite server queues; correlation
Summary: 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.