| Chinese agricultural insurance is still in the primary stage of development for the moment.As a part of agricultural insurance diversification mechanism,agricultural reinsurance plays an irreplaceable role in transferring agricultural risks.Chinese agricultural insurance develops rapidly in recent years;however,a variety of extreme weather disasters occur which make the Chinese agricultural reinsurance business gradually exposes to the accumulation of various risks,the overall insurance payment rate increases significantly.It seriously hinders the long-term and stable development of Chinese agricultural reinsurance.Agricultural reinsurer need to manage the systemic risk more efficiently in the way of developing more accurate actuarial models and designing more reasonable risk-sharing schemes to address these uncertain risks.The CIRC,the Ministry of Finance and the Ministry of Agriculture jointly carried out the revision of the agricultural insurance products in February 2016,with the theme of”expanding responsibility,guaranteeing and simplifying claims”.The absolute indemnity and cap of agricultural insurance are canceled,the absolute compensation standards in the difference growth stage and under the different conditions are raised,part of the regional premium and insurance rates become lower,the largest decline rate of which is almost up to 50%.Elimination of exemption and rate adjustment promote the further development of agricultural insurance,but the agricultural insurance companies are facing greater pressure in their solvency.The pressure from the reform of agricultural insurance is passed on to the reinsurance companies,and the increment in the repayment will make the agricultural reinsurance company pay more compensation with the different forms of reinsurance contracts.The main trend of the competition in insurance market focuses on the market service and technical level.At present,the actuarial technology in China's reinsurance industry still has a big distance compared with the developed countries.In the face of the increasing competition among the international reinsurance market,the problem is worthy of further study that how Chinese reinsurance industry can improve the professional level and provide additional value in product design,pricing and risk management thereby realize to expand market share and enhance the position in the international reinsurance market.The risk is more and more complicated with the emergence of new types of insurance products which increases the difficulty of management.If the risks are not be estimated accurately enough when designing the products,the reinsurance companies will also be challenged with the corresponding proportion of risk which comes from the mispricing.In the entire insurance business chain,the advantages of reinsurance more reflect from the data accumulation,modeling technique and product pricing.Therefore,,agricultural reinsurance companies should participate in the process of some innovative insurance products development,to provide more accurate actuarial technology and modeling support to the insurance companies such as the insurance contract design and rate determination to control the adverse selection and moral hazard which can also control reinsurance risk from the source of product design.There are many factors that affect the decision-making in business selection of agricultural reinsurer,This study mainly focuses on the aspects of risk measure,weather index insurance designing,premium principles and business selection criteria to proceed research.The method of actuarial modeling and mathematical deduction are used in this paper,combining with some econometric models for agricultural reinsurance companies to achieve optimal business selection.Through comprehensive and in-depth quantitative analysis on the above issues,agricultural reinsurance companies can establish more scientific risk assessment models and provide more accurate technical support for the insurance companies,reducing the adverse selection and moral hazard from the source of the insurance.This will be helpful to achieve long-term sustainable and stable development of agricultural reinsurance companies,and can also provide strong support to the Chinese agriculture and the safety of grain production.Specifically,this paper focuses on the following major issues from the perspective of agricultural reinsurance companies: Which risk measure can be used to optimize the benefits of insurance companies and reinsurer at the same time? How to minimize the risk before the weather index insurance product is reinsured by applying a more accurate model? When there are new agricultural reinsurance business,it is necessary for the agricultural reinsurance company to measure the aggregate risk of the new business and the existing business,then to decide if take the underwriting or not;if take the underwriting,what is the contract form and the premium principle to make the agricultural reinsurance company achieve the maximum profit? Based on the actuarial models of the above agricultural reinsurance business and the reasonable estimation of the parameters,the following conclusions are drawn:1,Two sided coherent risk measure assumes that rational investors will consider the risk appetite of counter parties which makes fully use of the information about the overall loss distribution;the risk appetite for the insurers and reinsurer can be considered at the same time,which is a unique advantage in analyzing the financial and insurance problems with multiple suppliers or demand parties who have different risk attitudes at the same time;when there are multiple reinsurance companies,it is still a consistent risk measure after the generalized convex combination of multiple two sided coherent risk measures,and under certain conditions,it has the properties of both the absolute deviation and semi-variance;it is especially suitable in dealing with the loss distributions with asymmetric and fat tail which is more common for agricultural reinsurance.2,The standardized insurance contract products are more easily underwritten by the international reinsurer,while the design of scientific and reasonable weather index insurance needs more technical support with high actuarial level.Agricultural reinsurance companies need to determine actuarial models from both perspectives of index design and contract design.(1)For the index design actuarial model,the rice growth cycle is further subdivided into six subperiods from three subperiods,which significantly reduces the basis risk;the effects of different weather factors on the crops at different growth stages were better captured by multiple linear regression models;using the BIC criterion to reduce the dimension of the weather factors and using the LASSO method to reduce the dimension of the growth circles,the high-dimensional data is reduced to 11 dimensions from 24 dimensions with the two-step regularizations,but the interpretation of the variance can still reach 93.97%.The weather index designed is both concise and highly related to crop yields using the above actuarial modeling,which can better transfer the weather risks for the agricultural production.(2)For the contract design model,the precise design of the payment structure contributes to the risk hedging effect of the weather index insurance contract.Crop yield data are often non-normal,skewed and kurtosis distributed with some extreme values,the tail risk is greater which make the least squares regression results be biased;furthermore,the relationship between the crop loss and the weather index are often non-linear.The quantile regression can get the robust result and also change the linear payout structure,making the insurance contract compensation structure more scientific,and then reducing the basis risk further.(3)Agricultural reinsurance companies are faced with data shortages during business selection analysis.In order to solve this problem,this paper first analyzes the different unit root test methods to determine the trend test method which is most suitable for small sample,then analyzes the trend after normalization of the data,and then do the nonparametric kernel estimation method to the yield and weather index with the PPS sampling method to further overcome the drawbacks of small sample data.These techniques contribute to improving the accuracy of the model in the case of small samples,making the pricing more accurate and provide better reference for the risk management of the agricultural reinsurance companies.Based on the two sided coherent risk measures,the risk hedging effect of the designed weather index insurance contract is measured to further examine the effectiveness of index selection and contract design.3,Pricing is difficult in agricultural insurance,after the risk is minimized through the above modeling process,when there are new reinsurance businesses to the agricultural reinsurer,some more scientific indicators are needed to measure the aggregating risk.In this paper,the standard deviation criterion of the tail is introduced into the field of agricultural reinsurance,and the reinsurance business is priced according to the standard deviation premium principle.Then the tail risk index is designed to compare and select the different business portfolios with corresponding co-reinsurance level and layers.This robust pricing framework is conducive to improving the long-term profitability of agricultural reinsurance companies.Based on the perspective of agricultural reinsurance company,this study tries to provide more appropriate and accurate models for the risk control of agricultural reinsurance companies using the appropriate quantitative analysis and mathematical models.This article is innovative in the following points:1,It is the first time to introduce the two sided coherent risk measure and apply it in the field of agricultural reinsurance practically.Two sided coherent risk measure has unique advantages compared with other risk measures: It can take into account but differentiated the risk appetite for the supply and demand side(insurance companies and reinsurers)at the same time.When there are multiple reinsurance companies,it is still a coherent risk measure after the generalized convex combination of multiple two sided coherent risk measures.The use of higher order probability weighting can better deal with the asymmetry and fat tail features in reinsurance loss distributions.It has not been applied to the insurance field so far except Chen Zhi-ping and Zhang Feng(2012)applied it into the analysis of stock portfolios.2,Based on the perspective of agricultural reinsurance companies,this study adopt the BIC and LASSO regularization in two steps to reduce the dimension for the high dimensional weather variables,the method of quantile regression is used to design the payment structure of weather index insurance contract which can overcome the drawbacks of the linear payment structure.The above techniques make the weather index insurance contract more scientific and transparent,and more easily to cede to the international reinsurers,improving the voice of Chinese agricultural reinsurance.3,The standard deviation premium principle is introduced into the field of agricultural reinsurance pricing which has a unique advantage in pricing the fat tail of the loss distribution in agricultural reinsurance business.The tail risk ratio index is designed for the first time and applied into the selection of the agricultural reinsurance business,it can help to minimize the ruin probability of agricultural reinsurance companies.The use of standard deviation premium principle and tail risk ratio in the field of agricultural reinsurance contributes to the actuarial models of agricultural reinsurance pricing.4,The number of agricultural reinsurance literature is small in Chinese literature.The existing research basically focus on the qualitative analysis,and furthermore,few researchers study agricultural insurance and agricultural reinsurance as a whole,which is not good to the precise pricing for reinsurance products as well as long-term stable development to Chinese agricultural reinsurance market.The quantitative analysis methods used in this paper are more comprehensive and systematic.This paper analyzes the specific business selection criteria from different points for agricultural reinsurance companies in the context of the real economic background of our country,to make the Chinese agricultural reinsurance companies minimize the ruin probability.With carrying out a detailed calculation,the overall analysis framework is complete and is also applicable to other types of insurance analysis. |
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