Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts

Author

Daniel J. Geiger
Akim Adekpedjou, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Comments

Missouri University of Science and Technology, Grant None

Keywords and Phrases

Catastrophes; IBNR; Markov renewal models; Markovian discount rates; Random thresholds

International Standard Serial Number (ISSN)

1573-7713; 1387-5841

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 Springer, All rights reserved.

Publication Date

01 Jun 2022