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

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.