Studying the return of Single or Periodic Risk Premium Temporary Life Annuities

Abstract

This paper analyzes deferred temporary annuities and deferred life annuities insured’s return. With both kind of actuarial transactions being conditioned to the insured’s survival probability; their respective profitability is random and depends on the insured’s survival probability distribution. We will define the expected return and, basing on the probability distribution of the random variable that we call the insured's benefit, we will obtain decision parameters that reflect the risk of both kinds of operations and its influence on that expected return. Our theoretical development will be carried out for single and periodic premiums, in all cases under the hypotheses of pure premium. Finally, we will present an empirical analysis of all the cases, showing the applicability of the results obtained, with the aim that the insured may avail himself with as much information as possible to make his or her decision in a random environment.