Semicontinuous endowment insurance premium valuation using quadratic fractional age assumptions

Abstract

The classic assumptions used to calculate fractional ages in valuing insurance premiums with payouts made immediately after death result in discontinuous probabilities of immediate death at integer ages because the assumption only applies to a 1-year time interval, specifically . The new assumption, namely the quadratic fractional age assumption, has successfully introduced continuity at integer ages. This study discusses the conditions for applying the quadratic fractional age assumption and its influence on the calculation of semi-continuous dual-purpose insurance premiums, where the policyholder's beneficiaries receive the sum assured if the insured individual passes away before the contract ends or receive protection if the policyholder survives until the end of the contract, with premium payments made on a monthly basis. Simulation results indicate that not all mortality tables meet the requirements for the quadratic fractional age assumption, where the value falls between . Only the Commissioners Standard Ordinary Table 1958 meets this criterion. Monthly premiums calculated using the quadratic fractional age assumption yield smaller values compared to premiums calculated using the constant force of mortality assumption and the uniform distribution of death assumption.