On Fitting Dependent Nonhomogeneous Loss Models to Unearned Premium Risk

Sébastien Jessup, Jean-Philippe Boucher and Mathieu Pigeon

North American Actuarial Journal, 2021, vol. 25, issue 4, 524-542

Abstract: Unearned premium or, more particularly, the risk associated to it, has only recently received regulatory attention. Losses linked to unearned premium, or unearned losses, occur after the evaluation date for policies written before the evaluation date. Given that an inadequate acquisition pattern of premium and approximate modeling of premium liability can lead to an inaccurate reserve around unearned premium risk, an individual nonhomogeneous loss model including cross-coverage dependence is proposed to provide an alternative method of evaluating this risk. Claim occurrence is analyzed in terms of both claim seasonality and multiple coverage frequency. Homogeneous and heterogeneous distributions are fitted to marginals. Copulas are fitted to pairs of coverages using rank-based methods and a tail function. This approach is used on a recent Ontario auto database.

Date: 2021
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DOI: 10.1080/10920277.2020.1776623

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