Insurance and copulas: an application to indemnity claims

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 in independence hypothesis. Calculations and estimates are based on a large dataset of an Italian non life insurance company.