The Research Of Loss Reserve Evaluation For Non-life Long Tail Insurance

The loss reserve of non-life long tail insurance is one of the most important liability items of the non-life insurance companies. The sufficient loss reserve is an important approach to keep the company in enough business solvencies. Because of the higher uncertainty and risks, the loss reserve evaluation for long tail is more difficult compared to the short tail. And also because of the different loss reserve features, loss reserve evaluation for long tail is quite different from the short tail. But in the CIRC's Actuarial Provisions for non-life insurance technical reserves, there's no differences between the long tail and short tail's loss reserve evaluation. This will lead to a deviation in the long tail loss reserve in the future, as the long tail grows rapidly in our country. So it is very vital to study the loss reserve evaluation methods for the long tail and give reasonable proposals to the CIRC.This article is focused on the actuarial techniques for the long tail loss reserve evaluation. It begins from the origin and feature of the long tail loss reserve. The definition of long tail and short tail is from the origin of the loss reserve. Therefore, in the first chapter, it analyses the loss reserve's origin at first: the reporting delay and the settlement delay. According to the delays and reserve evaluation time, the loss reserve can be divided into three parts: incurred but not reported (IBNR) reserve, case reserve and claim adjustment expenses reserve. And the long tail has a longer reporting delay and settlement delay compared to the short tail. So the long tail loss reserve evaluation must take the delay period and the inflation into account. This is the key difference between the two kind non-life insurance and this causes the feature of the loss reserve evaluation is quite different. Then the chapter analyses the detailed impact on the long tail loss reserve evaluation which from the two aspects of inflation: the economical inflation and the social inflation. Overall, the first chapter is the basement of the article.The second chapter analyses the basement of long tail loss reserve evaluation: the data preparation and analysis. For all the non-life insurance, it must collect data at first, then test the data and finally, analyze the data by the form of run-off triangles. The run-off triangle technique is the basement of modern actuarial loss reserve evaluation technique. Because of the importance of inflation, the basement of long tail loss reserve evaluation should include the analysis of the history inflation besides the above points. So it then discussed how to analyze the history inflation by the run-off triangle. On this base, with the reasonable forecast of future inflation, we can go on the evaluation of the long tail loss reserve.In the next part, the article analyzes the evaluation of the long tail loss reserve from two aspects. First it analyzes the inapplicable points for the long tail loss reserve evaluation in the CIRC's Actuarial Provisions. Then it introduces other applicable loss reserve evaluation methods for long tail and gives advices to the CIRC.The chapter three discusses the evaluation of IBNR reserve. The CIRC recommends four methods for IBNR reserve evaluation: the CL method, the PPCI/PPCF method, the PCE method and the B-F methods. These methods can be used to evaluate the long tail IBNR reserve, with taking the inflation adjustment into account. First it introduces the standard CL method and the inflation-adjusted CL method. And it analyzes the evaluation effect of the two methods through simulation data, including different level of simulation inflation rates and simulation loss data. The outcome proofs that the inflation-adjusted method of the CL method is effective to evaluating the long tail IBNR reserve. And then the chapter using this kind of inflation adjustment analyses the inflation-adjusted PPCI/PPCF method, the inflation-adjusted PCE method and the inflation-adjusted B-F method. The simulation data analysis'result shows that the inflation-adjusted PPCI/PPCF method and the inflation-adjusted PCE method are also effective to the long tail IBNR reserve evaluation. But the B-F method is hard to adjust the inflation appropriately.The chapter four analyses the evaluation of case reserve. It first discusses the case by case estimate method and the average value method which recommended by the CIRC can not reflect the long tail's future uncertainty and inflation risks. So they are not suitable for the long tail case reverse evaluation. Learning the result of the chapter three, the article analyses some other methods suitable for the long tail case reverse evaluation in the next part, including the PCE method, report-year loss delay method and tabular value method. These methods are based on the data run-off analysis and can adjust the inflation. So they can evaluate the long tail case reserve more objectively and accurately.The chapter five analyses the claim adjustment expenses reserve evaluation. First it analyses the evaluation of the direct loss adjustment expenses reserve. Besides the specified method by CIRC, the article introduces another two methods: the paid ALAE development method and the cumulative paid ALAE to cumulative paid loss method. Next the article discusses the evaluation of the indirect loss adjustment expenses reserve. The paid to paid ratio method specified by the CIRC is not appropriate for the long tail indirect loss adjustment expenses reserve evaluation, with the same reason analyzed in the discussion of the CIRC's case reserve methods in the chapter four. So the article introduces the operation-based Johnson method which is widely used in the U.S.A nowadays. It can provide a reference for our long tail loss adjustment expenses reserve evaluation.In the last chapter, the article analyses some key issues in the non-life long tail loss reserve evaluation practice and give some appropriate suggestions to the regulator. First the evaluators should pay attention to the tail loss development factor (LDF) when evaluating the reserves using any methods based on the CL technique. The accurate estimation of the tail LDF is the basement of accurate evaluation of the reserves. Then the article analyses the discount regulation of the long tail reserve evaluation world widely. Under the appropriate regulation, evaluating the long tail loss reserve with the appropriate discount rate can enhance the efficiency of the using of the insurance funds. This can promote the development of the long tail and the insurance company. In the last, with the results of the analysis above, the article gives some four advices to the CIRC, hoping promoting the development of the non-life long tail loss reserve evaluation and the regulation.