Wishart‐gamma random effects models with applications to nonlife insurance

Michel Denuit () and Yang Lu
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium
Yang Lu: University Sorbonne Paris Nord, Villetaneuse, France

No 2020022, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Random effects are particularly useful in insurance studies, to capture residual heterogeneity or to induce cross‐sectional and/or serial dependence, opening hence the door to many applications including experience rating and microreserving. However, their nonobservability often makes existing models computationally cumbersome in a multivariate context. In this paper, it is shown that the multivariate extension to the Gamma distribution based on Wishart distributions for random symmetric positive‐definite matrices (considering diagonal terms) is particularly tractable and convenient to model correlated random effects in multivariate frequency, severity and duration models. Three applications are discussed to demonstrate the versatility of the approach: (a) frequency‐based experience rating with several policies or guarantees per policyholder, (b) experience rating accounting for the correlation between claim frequency and severity components, and (c) joint modeling and forecasting of the time‐topayment and amount of payment in microlevel reserving, when both are subject to censoring.

Date: 2020-09-25
Note: In: Journal of Risk and Insurance - to appear, p. 39 (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020022

DOI: 10.1111/jori.12327

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