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Wishart‐gamma random effects models with applications to nonlife insurance
Author(s) -
Denuit Michel,
Lu Yang
Publication year - 2021
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/jori.12327
Subject(s) - wishart distribution , econometrics , censoring (clinical trials) , multivariate statistics , random effects model , context (archaeology) , diagonal , computer science , statistics , actuarial science , mathematics , economics , medicine , meta analysis , geometry , paleontology , biology
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‐to‐payment and amount of payment in microlevel reserving, when both are subject to censoring.