Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process
Copyright policy )Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process
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.
- University of Franche-Comté France
- Concordia University Wisconsin United States
- University Of New South Wales
- UNIVERSITY OF NEW SOUTH WALES
- UNSW Sydney Australia
330, incurred but not reported (IBNR) claims, Applied probability, 510, anzsrc-for: 40 Engineering, Incurred But Not Reported (IBNR) claims, infinite server queues, FOS: Mathematics, Queues and service in operations research, anzsrc-for: 46 Information and computing sciences, Applications of renewal theory (reliability, demand theory, etc.), 4901 Applied Mathematics, Probability (math.PR), Fractional processes, including fractional Brownian motion, anzsrc-for: 4905 Statistics, Infinite server queues, Correlation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 4905 Statistics, anzsrc-for: 49 Mathematical Sciences, fractional Poisson process, correlation, 49 Mathematical Sciences, anzsrc-for: 4901 Applied Mathematics, applied probability, Fractional Poisson process, Mathematics - Probability
330, incurred but not reported (IBNR) claims, Applied probability, 510, anzsrc-for: 40 Engineering, Incurred But Not Reported (IBNR) claims, infinite server queues, FOS: Mathematics, Queues and service in operations research, anzsrc-for: 46 Information and computing sciences, Applications of renewal theory (reliability, demand theory, etc.), 4901 Applied Mathematics, Probability (math.PR), Fractional processes, including fractional Brownian motion, anzsrc-for: 4905 Statistics, Infinite server queues, Correlation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 4905 Statistics, anzsrc-for: 49 Mathematical Sciences, fractional Poisson process, correlation, 49 Mathematical Sciences, anzsrc-for: 4901 Applied Mathematics, applied probability, Fractional Poisson process, Mathematics - Probability
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