Analysis of the calendar year effect in claims reserving : from ultimate to one-year perspectives

Abstract

This thesis studies the calendar year effect (CYE) on the estimation of incurred but unpaid claims (losses) which is required to calculate reserves for a single line of business and the overall portfolio in an insurance company. Three different types of CYE models including (i) common CYE (ii) independent CYE, and (iii) dependent CYE, are considered to develop the claim payment triangles for each business line. To this end, the CYE factor is added as a covariate to the systematic component of the incremental payments. A Bayesian method together with the plug-in estimates and also full Bayesian analysis are adopted for parameter estimations. Then, the aggregate reserves for the overall portfolio is obtained via Gaussian copula which captures a cell-wise dependence between lines of business. It is noted that reserve risk is analyzed from both ultimate and one-year perspectives. In particular, a simulation procedure is developed to quantify one-year reserve risk.

To illustrate the application of the proposed models, we use the data set from Schedule P of National Association of Insurance Commissioners (NAIC) which includes the claim payments for personal auto and commercial auto. Under different CYE models, the predictive (undiscounted) outstanding claim payments are obtained for each line of business and the overall amounts for the company. This result is related to the ultimate reserve risk which is recognized for the lifetime of the liabilities. Furthermore, the reserve risk at different confidence levels is analyzed in the one-year time horizon, which is more useful from the regulator's perspective. Lastly, we numerically demonstrate the performance of the full Bayesian method on reserve estimation.