Research On Installment Joint Life Insurance Actuarial Models Under Stochastic Interest Rates

In real life, people may face the risk of disease and death caused by accidents . Although the risk of death is difficult to predict individually, but as a group, the risk tend to share stability. As to insurance companies, the risk of death is difficult to predict for individual insurance-holder, but when dealing with group customers rather than individuals, the risk appears more discrete with more insurance-holders.Randomness exists in interest rate from the historical data with a lot of factors that affect it, thus it is difficult to use a precise mathematical method to describe the fluctuations in interest rates. In the traditional actuarial theory, the interest rate is fixed once taking effect.Since single life insurance policy is valid for decades long and the circulation of fund is no time-efficient, the impact of interest rates on the insurance company is very large. To meet the needs of social development, research on stochastic interest has aroused more scholars working on random interest rates.With the cost of living in nowadays society increasing, there come installments, for example, to buy a house. Previous life insurance is paid in year when many Chinese insurance company recently launched a kind of new life insurance that can be paid quarterly even monthly. Therefore, this paper is focused on installment joint life insurance actuarial models under stochastic interest rates .Firstly, this paper introduces some basic concepts of stochastic processes and life insurance actuarial models, and in the second place, it is digested carefully about simulation interest force accumulated function, taking the impact of the actual investment premiums and emergencies on interest rates into account and with the Wiener process and the Poisson process. A joint life insurance installment payment under stochastic interest rate mode is established, and the consumer price index is introduced into life insurance actuarial models to analyze the impact of inflation on the insurance. The two parts construct the additional life insurance actuarial models. Meanwhile, it is also given the net single premium life insurance policy premiums, reserves and specific expression of the insurance company's risk of loss.Thirdly, apply the specific insurance model above into practice under the assumption of Gompertz and UUD, which can be obtained of corresponding expressions. By means of numerical calculation, it can be analyzed the influence on premium and reverse about several factors like the benefits function, the number of installments and the span of insurance. At last,according to the data of interest rate changes over the years, the stochastic interest rate models are tested to be true,which means circumstances involved are along with the actual model. In conclusion, the paper is of theoretical significance and practical value.