Estimation of property and casualty business loss reserves by stochastic methods and financial effects on the insurance companies

Insurance companies can be faced with being unable to meet their future liabilities due to a failure to allocate the loss reserves at the right amount; therefore, the companies may suffer from capital difficulties in the future. In addition, loss reserves help companies to carry out their activities with the right decisions due to the direct effect of the loss reserves on the profit/loss balance of the companies. In this study, the loss reserve models for non-life insurance has analyzed and explained in general terms. Besides, theoretical model differences between deterministic and stochastic methods has been investigated. The Mack model, the Over-Dispersion Poisson distribution model and the Gamma distribution model as the stochastic models were compared with the Chain Ladder method, the Bornhuetter-Ferguson method and the Cape-Cod method as classical models. The application data analyzed in the study includes loss data of the motor liability insurances branch of all non-life insurance companies operating in Turkey. The loss estimation models used in the application are analyzed comparatively through the R program. The profitability of the motor liability insurance market in Turkey has been investigated with confidence intervals arising from reserve uncertainty. In conclusion, the best loss reserve estimate was obtained by using the over dispersed poisson bootstrap model.