An Analysis Of Reinsurance Pricing Under Fat-tailed Distributions

The function of risk management of Reinsurance market to maintain the stability of the direct insurance market and even to keep the robustness of the whole financial market system are both essential. Especially today, with coming of the financial globalization and social wealth accumulation and concentration coming, whether the demand of direct insurance market transferring risk, or the demand of other financial institutions or the whole system maintaining steady, are all contributed to the emergence of a high maturity reinsurance market. So far the domestic reinsurance market still cannot meet the needs of the growing rapidly direct insurance market, and all participants expect to mature reinsurance market more strongly. So the development of reinsurance would be the primary task of the domestic insurance market and the financial system construction.The domestic introduction of the new policy is also supporting the development of the reinsurance market. The Several Opinions on Accelerating the Development of Modern Insurance Service Industry, issued by the State Council in August of 2014, proposed to develop the regional reinsurance center (especially in the FTA for a trial), to encourage the innovation breakthrough of insurance products and technologies, and to strengthen the protecting function of reinsurance to domestic enterprises' overseas business to enhance the domestic reinsurers pricing right to speak in the global market. Ultimately it wants to grow the whole industry by developing the sound reinsurance market.How to promote the development of domestic reinsurance market, fundamentally? Improving reinsurance Actuarial level, which is the technical factors supporting the growth of domestic reinsurance market, is the key issue. At present, domestic reinsurance actuarial development is still lagging behind the developed countries'. Systematic reinsurance actuarial study is significant deficiency and this article highlights the lack of development of reinsurance pricing. A reasonable reinsurance pricing, which always follow the principle of sharing common interests and bear the same risk, is the basis for the reinsurance contract. When reinsurance Pricing, average expected loss estimating for reinsurance is a basic problem that cannot be avoided. And the estimation this article focuses is the Statistics considering joint risk benefits from original insurers and reinsurers. Early studies on optimal reinsurance is limited to only consider the interests of the insurer, while ignoring the reinsurer's. Since the establishment of reinsurance business relationship itself is a kind of cooperative behavior, we should be taking into account the interests of their respective risk. In estimating the average expected loss of reinsurance, for reinsurers, small probability of extreme loss risk analysis is an important task. Once the original insurance companies shift the huge risk to the reinsurance companies, the occurrence of extreme payouts or not will have a huge impact on the overall profits of the reinsurance business. Faced with a direct impact on the operational effectiveness of their own extreme loss management, reinsurance companies should choose a more reasonable loss distribution to comprehensively analyze the tail of the loss datum, and should carefully evaluate their reinsurance risk.This article introduces different distribution functions as tail loss analysis tool which is used into the empirical analysis of reinsurance risk assessment, and it wants to get the differences impacts on the reinsurance pricing and related risk management. In the article, it not only uses some common distribution functions as tail loss analysis, such as gamma distribution function and lognormal distribution function, but also uses the generalized Pareto distribution function which is specifically for the distribution fitting of tail loss. Meanwhile the generalized beta ? distribution function is introduced into the reinsurance tail risk analysis. The generalized beta ? distribution function is currently relatively small in insurance loss analysis, which can be seen as a relatively new introduction and add a new tool for the reinsurance risk analysis.By analyzing the different outcomes of excessive loss estimations from different loss distributions, this article tries to emphasize the special nature and importance of prudent reinsurance risk assessment, and expects to give recommendations for the reinsurance premium pricing and related risk management, and maybe bring some new information when CIRC develop reinsurance regulatory policy. Finally this article wants to provide some assistance and suggestions about reinsurance actuarial technology strengthening.This article generally comprises two portions which are reinsurance pricing theory, reinsurance pricing empirical analysis and its related policy recommendations.The first part includes introductions of both the reinsurance theory and the theory of tailed loss analysis. In the introduction of the theory of reinsurance, it mainly includes the reinsurance definition, classification and the reinsurance markets (domestic and international market) situations. Then this part analyzes the demand and function of non-life reinsurance market, and finally discusses the reinsurance actuarial issues, in particular the analysis of the reinsurance pricing. In the theory of tailed loss analysis, it mainly includes loss distribution theory and the tailed loss analysis theory, focusing on the introduction of four thick-tailed distributions as the tool to analyze the extreme risk later.The second part includes reinsurance pricing empirical analysis and its related risk management policy recommendations in two parts. In the empirical analysis, this article gives the non-proportional excess of loss reinsurance net premium pricings under four thick-tailed distributions, and also gives the four distributions' sensitivity analysis over extreme loss datum. In the recommendation, by the above empirical analysis, this part gives the related policy recommendations from original insurer, reinsurer and reinsurance regulator respectively.