Research On Family Multiple Life Actuarial Model Under Stochastic Interest Rate

As an important part of the financial system, the insurance industry is closely related to the public interest. In life insurance, interest-rate risk will bring about immeasurable risk for the insurance company. The theories and methodologies of the life insurance under the random interest-rate have been considered and always the hot topic of research in recent years. This paper establishes a combined life insurance actuarial model via the random interest rate.Firstly, this paper analyzes the domestic and international life insurance market face a variety of interest rate risk, explains the influence factors on life insurance business, and also points out the risk brought by the traditional assumed interest rate for the life insurance company is immeasurable.Secondly, this paper briefly introduces the related knowledge of life-insurance, and on all these bases, builds the binary (couples), the ternary (man and wife, children) survive models under different life conditions, and then gives common four death force analytical models.Thirdly, considering the influence of different information on the interest rate, constructing stochastic interest rate by interest force accumulation function: R(t)=δt＋βN(t)＋γG(t)(0≤t<∞) Where N(t) follows negative binominal distribution with parameters (k,p);G(t) follows Gamma distribution with parameters (u,v);N(t) and G(t) are independent;δdenotes the constant interest force,β,γ≥0 are independent constant. Based on this, we establish the completely successive whole life insurance actuarial net premium and reserve model of the family combined life insurance under different survive states. Finally, under the assumption of De Moivre:μx=1/(ω-x)(0≤x<ω), we obtain the specific expression of the life insurance actuarial model and simplify the calculation process of the life insurance premium. In order to verify the practical applicability of the annual level premium P(Axy)and the reserve,V(Axy)=Axy+t-P(Axy)axy+t,then we apply this model to the specific insurance practice.Through using the numerical calculation and the simulation of matlab, we explain the effect of the variety of the parameters in the model on the annual level premium and the reserve, and obtain the importance of the interest rate stochastic research and has good application value of the combined life insurance,the conclusion accord with insurance practice.