The Research And Pricing Of Couples Last Survivor Life Insurance

The last survivor life insurance for married couples means that both married couples are jointly insured as insured persons.In accordance with the insurance contract,all other family members are available as beneficiaries when both insured persons have an accident such as death,disability,illness and so on.This kind of insurance can not only manage the family finance,but also can save the family from financial crisis,stabilize the economic resources of the family and protect the family as a whole.The reasonable pricing of the couples last survivor insurance is the necessary condition for the products to be put on the market.The underestimation or overestimation of the actuarial present value of the couples last survivor insurance may bring huge losses to the insurance company.This paper is based on random mortality force and the assumption that the death of a couple is dependent.From the aspect that the death of anyone of a couple will inevitably affect the survivorship of survivor,this paper study the pricing of the last survivor life insurance.Assuming that before the first death,the couple's mortality force are independent and obeys the Ornstein-Uhlenbeck stochastic process,this paper design a probabilistic mechanism to determine the first death time in the couple and obtain the corrected mortality force of the survivor.The second death time is determined by the similar probabilistic mechanism.Based on this,the joint density function of the death time of both spouses is deduced by using the characteristics of Ornstein-Uhlenbeck random process.Based on the mortality data of 1994-2015 years in China and the United States,this paper estimates the parameters of the O-U random process of couple's death,and probes into the influence of the changes of three parameters on the joint density function of the death time for the elderly couples and young couples in China and the United States.The results show that the effects of bereavement are reflected through two of the parameters.On the assumption that the bereavement of couples in the United States and Chinese couples are the same,it is found that the actuarial present value of the last survivor insurance of the elderly couples in China is far higher than the actuarial present value of the last survivor insurance in the United States,while the difference of the actuarial value of the last survivor insurance of the young couples in the two countries is small.That means the regional difference for young couples is not obvious,and the regional difference of the bereavement of the elderly couples is very obvious.The bereavement influence of the American elderly couples may be weakened by the first-class medical level in the United States.Therefore,for different countries and age groups,bereavement affects the actuarial present value of the last life insurance for couples.Finally,this paper separately calculates the gross premium for the survivor's insurance when the insured couples are Chinese or American,old or young,and compares it with the gross premium under independent conditions.The results of the analysis show that,under dependent assumptions,the growth rate of gross premiums for young couples is lower than the growth rate of gross premiums for older couples,which is also consistent with the recognition that the effect of bereavement between older couples is higher than that between young couples.