Actuarial Analysis Of Life Insurance Under Stochastic Interest

The interest rate is assumed fixed in the traditional actuarial theory, but the interestrate is random in fact, it will change with the changes of economic environment and policy.Under the increasingly volatile financial market environment and the increasinglycompetitive environment of the life insurance market, the measurement, prediction andmanagement of interest rate risk become more important. So the research on actuarialtheory under stochastic interest has become one of popular topics for both researchers andpractice in life insurance.Based on the Summary of former research achievements of stochastic interest rate,this thesis first used reflected Brown motion combined with Poisson process, reflectedBrown motion combined with negative binomial distribution to describe the randomness ofinterest rates respectively, then further studied actuarial models of continuous lifeinsurance under single life state and double life states. We obtained the general explicitexpression of actuarial present value, annual premium and pure premium reserve for lifeinsurance and annuities under two kinds of interest models. We analyzed the influence ofparameters in stochastic interest model through data simulation through taking term lifeinsurance and annuity as examples. As for the situation of double life states, we consideredthe individuals were independent and dependent with Frank copulas, then studied theactuarial present value of life insurance and life annuities of the joint survival status andlast survivor status respectively.