The Application Of The Copula Function On The Family Joint Insurance

In this paper, to consider the family factors in family joint insurance at first. The future development of a couple’s survival will be configured to Markov model. Think about all the transfer mode within the states of this model,we find transition probability matrix of this mode. And Then deal with the relationship between transfer strength and transfer probability,We get the method to calculate all the transition probability of this matrix.And then we use transition probability to show the multi-life actuarial functions of the states of survival condition and the last survivor. We finally get the actuarial present value of the family joint insurance annual premium. But in this process owing to we simple processing the relations among individuals independently lead to cannot get high premium. In order to better meet the actual situation. This thesis uses multiple life function symbols which has improved. Unified the conditions of the actuarial symbols of single life and binary life. Combined with the binary conditions copula, to improve the conditions Archimedean copula, then get the Archimedean copula function and its generator in the same conditions. Then use the condition Archimedes copula function to deal with the correlation between the individual of joint life insurance. Make a study of family joint insurance model under stochastic interest rate. We can get the actuarial present value of its level annual premium. And given instance of the application of actuarial present value of the level annual premiums which deal with individual correlation with different methods.In this paper, the following work has been done:1. The future development of a family will be configured to a Markov model, and it will be as family factors introduced into joint life insurance actuarial model.2. Has improved the traditional multiple life function symbols. Unified single life actuarial notation and multi-life actuarial notation conditions; And in the uniform conditions introduces the conditional Archimedean copula to show relationship between family members in joint life insurance3. In response to these two cases above given the family joint insurance annual premium pricing respectively. Compare and analysis with ordinary family life insurance through the examples.