Measure,Influences And Management Of Longevity Risk

The paper is written in order for initial quantization of longevity risk faced by annuity business of life insurance companies and in order to explore solutions of the life insurance companies under the longevity risk accordingly. Obviously, the quantization of a longevity risk is the core of this paper. For this reason, in the paper, the quantization of longevity risk is divided into three stages:at stage1, the longevity risk is defined theoretically and divided into an individual longevity risk and a combined longevity risk which are respectively analyzed theoretically, relations and differences between the individual longevity risk and the combined longevity risk are discussed, the combined longevity risk is selected as a main research object, and, based on this, relations between the longevity risk and population aging are described and necessity in reasonable prediction of future death rate is proved; at stage2, after collecting national data of death rate according to the gender and age from1994to2011in our country, a Lee-Carter model and a Coale-Kisker model are selected to predict the death rate which is different in gender and age in our country in the future. In the prediction, the death rate of an age group from1year old to79years old is predicted by the Lee-Carter model and the death rate of a high-age group is predicted by the Coale-Kisker model. In operation of the Lee-Carter model, data of the death rate which is different in gender and age is preprocessed at first and the death rate in the data is translated into a center death rate as required in the Lee-Carter model. Based on this, Matlab software is used for Whittaker smoothing of the center death rate so that a life table of each year can satisfy good mathematic properties and life rules. After that, a Lee-Carter model is set up for the center death rate after smoothing, three parameter sequences are estimated, wherein two of them are influenced by the age while the rest parameter sequence only varies with time. The parameter sequence which only varies with time is subjected to time sequence modeling. Through comparison of an ARIMA model and an ARMA model with trend terms, the ARMA model with trend terms is finally selected. After this, Eviews software is used for parameter estimation. ARMA model structures with the best effect are selected respectively for males and females. A future estimated value of the parameter sequence is obtained and substituted into the Lee-Carter model. At last, the estimated value of the center death rate of people from1year old to79years old for different genders and ages from2012to2025are obtained. As for the high-age population group from1994to2025, the Coale-Kisker model is used to estimate the center death rate. In the end of this stage, the center death rate for people from1year old and110years old which is estimated by the Lee-Carter model and the Coale-Kisker model is translated into a death rate for following-up research; at stage3, based on the existing death rate and in combination with the future death rate data stated before, gaps of annuity pricing and provisioning in view of death rate improvement and without consideration about the death rate improvement are compared through specific cases (at the beginning of1994, males and females at55years old purchased annuity products to be paid10years later), in order to initially quantize the longevity risk contained in annuity business of life insurance companies.Through analysis of the above three stages, results of initial quantization of longevity risk in annuity business of life insurance companies are as follows:with an assumed interest rate of2.5%, the gap of full-amount pure premium paid by males is18.70%, the gap of pure premium expected to be paid by males is18.34%, the gap of full-amount pure premium paid by females is13.11%, the gap of pure premium expected to be paid by females is12.91%. For both the males and females, in each annuity payment year, liability reserve funds to be withdrawn are always insufficient continuously. According to the case, the longevity risk in annuity business of life insurance companies is initially quantized and it is indirectly shown that annuity pricing and withdrawal of liability reserve funds will be insufficient, relatively big death difference loss is generated and development of annuity products is restrained if annuity products of life insurance companies fail to pay full attention to continuous improvement of the death rate.Based on the relatively rigorous longevity risk which may be faced by annuity business of life insurance companies, the author proposes management manners of longevity risk of life insurance companies and basic ideas of longevity risk management in our country, wherein the management manners of longevity risk of life insurance companies include design of annuity products with natural hedges of death rate, application of reinsurance, vigorous promotion of participating insurance, restriction on insurance age of annuity products and securitization of longevity risk; the author emphasizes a leading role of governments in proposition of basic ideas of longevity risk in our country and thinks that governments shall promote implementation of deferred income taxes of endowment insurance, shall set up professional organizations, shall provide and predict death rate data and compile death rate indexes, and shall support construction of a securitization market of the longevity risk. At the same time, life insurance companies shall continuously adjust their own longevity risk management measures according to the longevity risk management measures of governments in order that their annuity business can be developed healthily, development of annuity market can be promoted and most of consumers can obtain benefits at last.