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Article Dans Une Revue European Journal of Operational Research Année : 2019

Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process

Jae-Kyung Woo
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Résumé

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.
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Dates et versions

hal-01682960 , version 1 (12-01-2018)
hal-01682960 , version 2 (06-12-2018)

Identifiants

Citer

Eric C K Cheung, Landy Rabehasaina, Jae-Kyung Woo, Ran Xu. Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process. European Journal of Operational Research, 2019, 276 (2), pp.582-601. ⟨hal-01682960v2⟩
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