On the distribution of stochastic life annuities with application to Philippine mortality data

• Main Authors: Ceniza, Rochelle Patricia L., Co, Kaiser Timothy C.
• Format: text
• Language: English
• Published: Animo Repository 2009
• Subjects: Life annuities > Philippines > Mathematical models; Mortality > Philippines > Mathematical models; Mortality > Philippines > Forecasting; Mortality > Philippines; Statistics and Probability
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/5229
• Institution: De La Salle University

In the area of life contingencies, life annuities are computed by treating mortality as a random variable and the force of interest as a constant. However, the financial environment in which the annuity is exposed in can change the rate of interest because of inflations and investment failures. This is further emphasized by the length of time life annuities take place in, which is usually in decades.Stochastic life annuities were introduced to quantify the added risk incurred by insurance companies by treating the force of interest to be random as well. Different techniques were devised to determine the distribution of this type of annuity but recently, the concept of comonotonicity was introduced to actuarial applications in which sums of products of random variables are ordered to approximate the distribution of life annuities.This paper gives emphasis to the said methodology and aims to give explanations and proofs to the theorems used in determining convex bounds for stochastic life annuities. Moreover, application of these concepts to Philippine mortality data is discussed by comparing stochastic life annuities to traditional life annuities. Further analyses made in the paper showed that life annuities assuming a stochastic force of interest give higher returns compared to the constant interest example, which would have implications for the existing life annuity business.