| Since China Reinsurance Corporation founded in 1999, reinsurance market has been larger in China. When we joined WTO, we promised that we would cancel legal reinsurance gradually in 4 years, that is, legal reinsurance would be canceled after 2007 in China. And our reinsurance market has faced huge challenge and also opportunities. We have already done a lot of research in reinsurance. At present, our reinsurance market has a good prospect, but reinsurance began later in China, so demand is much more than supply in reinsurance market.Because of above, I want to try my best for research in reinsurance. I summarize correlative theory about reinsurance and simple formulas of premiums of the largest claims reinsurance (LCR). Based on formulas of net premium under exponential claims sizes, I change one parameter, and get the new formulas of net premium and calculate premium rate.This paper has four parts.According to the data of "5.12" Wenchuan earthquake,I illustrates the practical significance of reinsurance in the first chapter. China is a country prone to natural disasters, which requires a sophisticated security system. However, the reinsurance in China started relatively late, compared to British which established reinsurance company in the seventeenth century, the reinsurance industry in China was 300 years behind. In recent years, with the deepening of reform, the economic has a rapid development, and China has established our own reinsurance company - China Reinsurance Company, marking the beginning of the insurance industry in China.China Reinsurance Company will lead the development of China's reinsurance industry. However, due to the reinsurance industry in China is short, and the foreign reinsurance companies are much more stronger than ours. This chapter reviewed the literature of reinsurance, introduced domestic and foreign scholars'studying on the reinsurance and some of the findings. Then simply illustrate the structure of the paper and the main contents of each chapter. At last the innovation and weaknesses are described.I introduce correlative theory about reinsurance, including the definition, sorts, function and the development in the world, especially some developed reinsurance markets. Reinsurance means insurance companies often seek reinsurance to protect themselves against catastrophic losses. According to different standards, reinsurance can be classed to different kinds. But proportional reinsurance and non- proportional reinsurance are common. Reinsurance is important not only in finance but also in the whole society. The document signed by China Insurance Regulatory Commission on June 1st of 2007, raising the function of reinsurance first time, those are dispersing risk, collecting capital, and transferring technique. In this paper, I will describe these three functions detailedly. Reinsurance has formed a few developed areas, these are Europe reinsurance market, North America reinsurance market, Asia reinsurance market and other reinsurance market. And in the first part of this paper, I will introduce the center and development of these big reinsurance markets. At the end of this part, I will introduce the development of the reinsurance in our country.The third part is the important part of this paper. Firstly, I introduce the definition of LCR. LCR is the short of largest claims reinsurance, and it means of all claims, the reinsure pays the sum of the p largest claims, and p is a decided constant. And discuss the formulas of net premium under discrete and successive claims size separately. And under the successive claims size, I introduce the formulas of Pareto claims sizes, exponential claims sizes and Wei bull claims sizes. In this paper, there is the research and summarization of characters of LCR, including the decision of parameter p and the up limit of the net premium.The last part is the center of this paper. We give the formulas of net premium of LCR under kinds of conditions in the third part. In the fourth part, we suppose the Poisson claims number distribution and Exponential claims sizes distribution. And according to the formulas given by Erhard Kremer in the third part, I establish new model after changed numerical value of the parameter. I calculated the net premium and premium rate under this model and gave a short analysis. The ratio of net premium of reinsurance and net premium of insurance we call it premium rate. During the calculation, we supposed different numerical values of the parameters, so we got the different numerical result. Though we can get numerical value of net premium under this model, because of the strict restrict conditions, this model can't be used into the practice simply, and the result should be corrected.This paper summarized basic theory of reinsurance, and discussed the formulas and characters of LCR. Erhard Kremer researched thoroughly in this problem. And I established a new model according to the formulas he gave in the given condition, what is the Poisson claims number distribution an. Exponential claims sizes distribution, when I changed the numerical values of the parameters, and that is the innovation of this paper. I calculate the net premium according to this model and statistic software. And my calculation shows the usability of this model, further, we know LCR has high usability according to my research.The research of the calculation of net premium of reinsurance is full of challenge, and it needs the hard work of the scholars in the society. I hope this paper can be useful to this problem. In the theory and practice of actuary, there still are many important problems need research, and these also needs he hard work of the scholars in the actuary area.There are many shorts or mistakes in this paper, for example, the summarization of methods isn't so detailed and the theory of reinsurance is too old and so on. Faced to these shorts, I beg the apologize of the readers, and hope your precious opinions to make progress together. |
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