Discussion On The Application Of Copula Function On The Calculation Of Group Life Insurance

In recent years, with the rapid and steady development of insuranceindustry of our country, studies on group life insurance are unprecedentedactive. It can often be seen that many warrantees share one contract,namely multi-life condition insurance, when deal with the daily insurancebusiness. The present pricing method of such contract is to simply sum theindividual life function and then get the joint function, which supposes thatindividual life in each group is independent. But as a matter of fact there'remany economic, marriage and even blood relationships between eachrelated individual life, which leads to certain dependent relationshipsbetween each future-life-time random variable, and which will definitelyinfluences the pricing of the contracts. How to make reasonable price forthese insurance products? Copula function provides an importanceinstrument to solve this. A Copula function will connect joint distributionsof several random variables with their marginal distribution respectively.We can well analyze and cope with the dependent structure problem ofrandom variables in probability statistics by utilizing the Copula function.There're five chapters in this paper. Chapter 1 describes the research situation about this topic both domestic and overseas, including theresearch on Copula function and the life insurance, points out that there'recomparatively rare studies on the multi-life stature contracts by utilizingthe Copula function, and finally derives the meaning of our research.Chapter 2 introduces the life function (both single-life and multi-life), lifetable and Copula function in detail. After displayed many kinds of Copulafunction, I find that the Archimedes function is the most effective one whenconsidering our researching purpose. Meanwhile this paper derives part ofthe nature of the Archimedes function family and elaborates theeffectiveness of Copula function's coping with the dependent structure ofrandom variables. Using Archimedes function, Chapter 3 chooses differentparameters and different Copula functions and forms two basic joint lifetables of multi-life condition, the joint life table of the last-survivor staturesand the joint life table of joint-survivor status. Based on these comparisonsof the joint-survivor function between the independent individual of thegroup and the dependent one was carried out. Chapter 4 gives the definitionand standard form of the annuity, derives the calculating formula of themulti-life insurance annuity and the formula of the pay, insurance premiumand the insurance premium reserve fund of two basic contracts in multi-lifeinsurance. Chapter 5 is the applied case analysis, which analyzes a problemabout the net premium and insurance pay of endowment contracts and isaffirmed with a practical example. At last it derives the bound of the limitedannuity.This paper discovers that Copula function is very effective when copewith the relevance between the individuals of group life insurance, made acomparison of the joint life table between the related individual andindependent one, the probability of the former is larger than the latter. Byanalyzing one endowment contract, it found that, when other factors are fixed, the higher relativity of the individual life, the larger the averageprepaid net premiumΠand the smaller insurance payment D, S. It alsofound that it will make the average prepaid net premiumΠlower, theinsurance payment D,S higher and the hurts the legitimate interest of theinsurance company when the interrelated individual are treated asindependent ones. Finally it derives the bound of the limited annuity.