Modeling outstanding claims in dependent run-off triangles considering calendar dependence

V, a loss reserve is a prediction of the amount an insurer will need to pay for future claims. Researchers have been exploring methods to incorporate dependencies among multiple loss triangles to improve the accuracy of outstanding claim prediction. This study aims to predict outstanding claims in dependent run-off triangles by considering the dependence among the outstanding claims paid in each run-off triangle.

The study considers the dependence among corresponding outstanding claims in run-off triangles related to different lines of insurance. It also takes into account the calendar year of payment of claims, in addition to factors such as the year of claim occurrence and the number of years of delay in payment. Two methods are used to model the inter-triangular and intra-triangular dependencies. The first method involves modeling the dependence among triangles by using a multivariate distribution for outstanding claims in the corresponding cells of run-off triangles. The calendar dependence within each run-off triangle is incorporated by adding a calendar year effect factor to the mean of the outstanding claims distribution. The second method uses a multivariate distribution for the outstanding claims of the calendar years corresponding to run-off triangles, capturing both types of dependence. Bayesian approach and Hamiltonian Monte-Carlo sampling methods are employed to estimate model parameters.

The study utilizes data from an Iranian insurance company on outstanding claims in car body insurance and third-party car insurance from 2012 to 2015. The two methods of calendar dependence modeling are compared using a scale mixture multivariate distribution with normal marginal distributions and copula dependence. The mean absolute percentage error is used to measure the accuracy of the prediction. The results show that using a multivariate distribution for calendar dependence modeling leads to a more accurate prediction compared to adding the calendar year effect factor to the mean model.

Based on the findings, it is concluded that modeling the calendar dependence among outstanding claims in run-off triangles using a multivariate distribution improves the accuracy of reserves prediction compared to using the calendar year effect factor. This approach can enhance the prediction of outstanding claims and contribute to the insurer's profitability and solvency.