Two-part D-vine copula models for longitudinal insurance claim data

Lu Yang, Claudia Czado

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In short-term nonlife (e.g., car and homeowner) insurance, policies are renewed yearly. Insurance companies typically keep track of each policyholder's claims per year, resulting in longitudinal data. Efficient modeling of time dependence in longitudinal claim data will improve the prediction of future claims needed for routine actuarial practice, such as ratemaking. Insurance claim data usually follow a two-part mixed distribution: a probability mass at zero corresponding to no claim and an otherwise positive claim from a skewed and long-tailed distribution. This two-part data structure leads to difficulties in applying established models for longitudinal data. In this paper, we propose a two-part D-vine copula model to study longitudinal mixed claim data. We build two stationary D-vine copulas. One is used to model the time dependence in binary outcomes resulting from whether or not a claim has occurred. The other studies the dependence in the claim size given occurrence. Under the proposed model, the prediction of the probability of making claims and the quantiles of severity given occurrence is straightforward. We use our approach to investigate a dataset from the Local Government Property Insurance Fund in the state of Wisconsin.

Original languageEnglish (US)
Pages (from-to)1534-1561
Number of pages28
JournalScandinavian Journal of Statistics
Issue number4
StatePublished - Dec 2022

Bibliographical note

Funding Information:
The authors are grateful to the reviewers for insightful comments leading to an improved article. Czado's work was funded by the German Research Foundation (DFG CZ 86/6‐1).

Funding Information:
German Research Foundation,DFG CZ 86/6‐1 Funding information

Publisher Copyright:
© 2022 The Board of the Foundation of the Scandinavian Journal of Statistics.


  • mixed data
  • property insurance
  • stationary


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