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Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims

Published online by Cambridge University Press:  24 April 2023

Jonas Crevecoeur Open the ORCID record for Jonas Crevecoeur [Opens in a new window] ,
Katrien Antonio ,
Stijn Desmedt  and
Alexandre Masquelein
Jonas Crevecoeur
Affiliation:
Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
Katrien Antonio*
Affiliation:
Faculty of Economics and Business, KU Leuven, Leuven, Belgium Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands LRisk, Leuven Research Center on Insurance and Financial Risk Analysis, KU Leuven, Leuven, Belgium LStat, Leuven Statistics Research Center, KU Leuven, Leuven, Belgium
Stijn Desmedt
Affiliation:
QBE Re, Bruxelles, Belgium
Alexandre Masquelein
Affiliation:
QBE Re, Bruxelles, Belgium
*
*Corresponding author. E-Mail: katrien.antonio@kuleuven.be
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Abstract

Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life insurance pricing tackles these right censored data via a two-step procedure. First, best estimates are computed for the number of claims that occurred in past exposure periods and the ultimate claim severities, using the incomplete, historical claim data. Second, pricing actuaries build predictive models to estimate technical, pure premiums for new contracts by treating these best estimates as actual observed outcomes, hereby neglecting their inherent uncertainty. We propose an alternative approach that brings valuable insights for both non-life pricing and reserving. As such, we effectively bridge these two key actuarial tasks that have traditionally been discussed in silos. Hereto, we develop a granular occurrence and development model for non-life claims that tackles reserving and at the same time resolves the inconsistency in traditional pricing techniques between actual observations and imputed best estimates. We illustrate our proposed model on an insurance as well as a reinsurance portfolio. The advantages of our proposed strategy are most compelling in the reinsurance illustration where large uncertainties in the best estimates originate from long reporting and settlement delays, low claim frequencies and heavy (even extreme) claim sizes.

Keywords

Non-life pricingnon-life reservingstatistical and machine learning methodsreinsuranceoccurrencereporting and development of claims

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 2 , May 2023 , pp. 185 - 212
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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