The Application Of Copula In Actuary Of Insurance

Copula was the dependence structure function of multiple random variables. Copulahad obvious advantages compared with the joint distribution. Because of it separateddependence structure away with marginal distribution form joint distribution. So we canstudy dependence structure more clearly.At the same time, we could structure themultidimensional distribution more flexibly by copulas. In addition, the copula could alsoconstruct many useful measures of dependences.Due to the excellent properties and high application value of copulas, many scholarshad devoted to the research of copula theory and application, and they had finished a lot offruitful work. The application of copula becomes more and more maturely at abroad.Scholars had achieved fruitful results in the financial and insurance field. However, mostof the domestic research of application of copula in insurance focused on the ruin theory.There was few research applied copula to the actuarial practice.And then taking into thedifference between reserves from current Chinese financial system and reserves fromInternational standard actuarial rules, we applied Copula into the calculation of unearnedpremium reserves in this paper. The main contents and results were as follows:1. Firstly, we introduced the definition and basic theorem of Copula. Then we gaveseveral classes of classical copula. Finally we introduced three kinds of measures ofdependence which were described with copulas and gives the measures of some classicalcopulas.2. Analyzed the characteristics of Archimedes copula.Especially analyzed thecharacteristics and suitable range of Clayton copula. Finally gives an iterative calculationmethod of the parameter of Clayton copula.3. Used Clayton copula to establish insurance model, and then calculated the VaR ofaggregate claim risk using stochastic simulation under a given confidence level, whichconsidering as aggregate reserves. Then compared with the results of the traditionalassumption, we found that the Clayton copula method was more applicable, more accuracy,and could solved the problem of the shortage of reserves.