The Life Insurance Actuarial Model Under Random Interest Rate

Actuarial science applies the knowledge and principles of mathematics, statistics,fmance,insurance and demography in the quantitative analysis of all aspects wthin the management of the insurance industry,providing scientific basis and tools for raising the level of management and making strategies.With the development of insurance,actuarial science is more and more important.Life insurance is a long-term business,interest rate is an important factor in calculating of premium and reserves.The traditional actuarial theory mainly use d-eterministic interest rate.However,with the rapid development of finance,interest ra -te changes fast with market,policy and so on,so considering random interest rate -s in life insurance is necessary.This article focus on presenting ARCH for modeling the force of interest, combining the random mortality to calculate the premium and reserves,using numerical simulation to analy the necessity of the random interest rate, and compare the calculating of premium and reserves under constant rates,ARMA model and ARCH model, reflect the practicability of ARCH model.On the basis of single policy,we can focus on measuring of the premium and reserves of a portfolio under the randomness of interest rate and motality,according to the reality that life insurance often sell a large number of policies to reduce the risk insurance.Considering the homogeneous portfolio,getting the limit distribution of the future average loss variable, and a numerical simulation is given,then providing theoretical support to the operation of insurance companies.