Actuarial Pricing Mechanisms Under Advanced Demographic Mortality Rate Intensity Function Involving Analytic Heligman-Pollard’s Third Law

Abstract

The objectives of this study are to derive actuarial present values of whole life annuity, whole life insurance and net level premiums. The net premium policy value on a scheme in force within period   years after it has been incepted represents the expected value at the time of the net future loss random variable that does not incorporate any allowance for expenses. The net premiums estimated on the policy value basis are obtained using the equivalence principle and not the actual premium paid. Computational evidence from the results reveals that the whole life annuity-due is the discounted survival state, showing the insured’s remaining potential to finance mortality risk through time. The whole life insurance value is the price of death claim where value increases as mortality increases and the time horizon declines. At age , while  and small magnitude of the premium is because the probability of death is very low, expected claim cost is minimal and payments are spread over a long premium-paying period. The male premium is higher than the female premium because of higher mortality rate intensities and hence . Therefore, this reflects pure mortality-driven pricing under the equivalence principle. The premium monotonically increases for both sexes at age  aswhile while at age ,  and . At age and. This increase is actuarially consistent with the equivalence principle​. The function​ increases because of higher probability of death and ​ decreases as a result of shorter premium-paying period. Hence the ratio grows rapidly at advanced ages.