Loss-Alae modeling through a copula dependence structure

After having described the mathematical background of copula functions we propose a scheme useful to apply a particular family of copulas – the Archimedean copulas – to indemnity payments and loss expenses of an insurance company with the aim of obtaining their joint probability distribution. The joint distribution is used to calculate – via Monte Carlo simulation – the premia of a reinsurance strategy in presence of policy limits and insurer’s retentions. Results coming from this strategy are compared with those obtained from the independence hypothesis. We also describe the procedures needed to estimate the parameters of our model. Calculations and estimates are based on a large dataset of an anonymous Italian non-life insurance company. Empirical results show that the correct way to model dependence through copula functions permits to avoid the undervaluation of reinsurance premia. Finally, we observe that the relative simplicity in estimating the right copula from empirical data and the use of algorithms able to be programmed also on a common PC makes this probabilistic instrument easy to be used by insurers and reinsurers to improve their valuation “ability” and to realize more efficient and precise estimation of their assets and liabilities.