Back-testing approaches of claims provisions best estimates in Non-Life under Solvency II

One of the essential goals of the actuaries is to build an adequate model to predict the best estimates of reserves for unpaid losses. However, the differences between the predicted values and the actual values are actually volatile. The actuaries have to calibrate the reserving models frequently to adapt them to the new information. The questions of this master thesis are: - How do we know whether the best estimates are appropriate or not? - Are the deviations between the best estimates and the observed values acceptable? If there are significant deviations, what are the reasons behind them? - Are the calibrations of the reserving model effectively appropriate? - If there are many reserving models, which model has the most suitable best estimates and fits best the historical data? Back-testing is an important part of the validation process, in order to compare the predicted values with their observations in practice, identify the significant deviations that may be due to the deficiencies in modeling, or maybe from other reasons. The aim of this master thesis is to study and develop an appropriate back-testing approach, which defines the procedure to evaluate the provision best estimates compared to the experiences in practice, the quality of the reserving model, and its underlying assumptions,... then use this assessment to give recommendations to improve the actuarial valuation methodology if necessary. In practice, the best estimates differ normally from the true losses. In order to know what deviations are acceptable or unacceptable, it is required to analyse the confidence intervals of best estimates, in which the majority of true values fall in. That is why this thesis have studied four different stochastic methods to measure the uncertainty of the best estimates, such as Mack's model, Bootstrap ODP, Bootstrap on Mack's model, and the Bayesian method. Due to the limitation of internship duration, only the first three stochastic methods are implemented to the back-testing tool (coded in R programming language). The Bayesian technique is still in development. Based on different ideas to evaluate the best estimates, this thesis studied four principle back-testing approaches: Traditional, Retrospective, Denuit-Charpentier and Merz-Wüthrich approaches. Whereas the Merz-Wüthrich back-testing approach is based on the prospective idea of claims development result (CDR) of Merz-Wüthrich to evaluate the pertinence of reserving model when having the new information in data, the other back-testing methods review the best estimates in the retrospective vision, compare the predicted values with the observations in each period of development. This project-thesis developed also a tool of back-testing. It contains the different back-testing methods, that can be applied to back-test the best estimates of different lines of business in Non-life. The actuaries are free to choose what back-testing method to evaluate the models. However, it can be concluded that there is no best back-testing method. This method may be appropriate for this model of this line of business, but not apt to another model of a different risk scope. Each back-testing approach has its advantages and limitations. Based on the uncertainty of stochastic methods, and the randomness of the cash-flow overtimes, the result from the back-testing approaches is an uncertainty analysis. It is important to remember that the back-testing result provides just information, maybe not the truth. Hence, before back-test the models, it is required to identify and validate the relevant underlying assumptions of the actuarial model, of the used stochastic methods applied in back-testing tools as well, and the unchanged systemic environment assumption. Also, the validation of data quality, the detection of outliers are highly recommended to do besides the back-testing. Understanding the underlying assumptions, limitations of the reserving models, and the back-testing methods before using them is really necessary. This can help the actuaries explain the reasons for significant deviations of best estimates, recognize the risk of bias estimations, ... From that, they can give a full assessment, with the appropriate recommendations to improve the actuarial model or change the old model to another model with new assumptions, which fits better the data.