The Study Of The Heavy-Tail Risk Models And Their Application In Social Security

According to the two representative directions of risk theory: the heavy-tail risk modeland the risk model under certain economic condition, main content about the paper is: Basedon the definition of heavy-tail distribution and heavy-tail classes, we have proved the naturetheorem of heavy-tail classes with another methods; According to renewal risk model, wehave proved equal formula of its bankrupt probability in value with another methods; and thenhave promoted equal formula of its bankrupt probability in value about equilibrium renewalrisk model of heavy-tail, delayed renewal risk model of heavy-tail and compound renewal riskmodel of heavy-tail. There are some important political and economic and social significancein social security, the key about social security is how to keep the balance of the fund aboutsocial security. The changes of economy can deeply influent the balance of the fund aboutsocial security. Through study of all-above risk models, At last, we have found the new riskmodel of social security. It is double delayed renewal risk model. Hence, in order to settle thequestion of collection about fund, we have proposed the adapted and accumulated mode andbuilt its mathematical model. According to the model, we have analyzed the social security ofour country and proposed some policy suggestions.