We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event's level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and reported claims.
D. J. Geiger and A. Adekpedjou, "Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts," Methodology and Computing in Applied Probability, vol. 24, no. 2, pp. 815 - 829, Springer, Jun 2022.
The definitive version is available at https://doi.org/10.1007/s11009-022-09950-5
Mathematics and Statistics
Keywords and Phrases
Catastrophes; IBNR; Markov renewal models; Markovian discount rates; Random thresholds
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2022
Missouri University of Science and Technology, Grant None