The bounds of bivariate distributions on joint-life and last-survivor annuities

• Main Authors: Manzo, Karen Valerie G., Tiu, Kenneth N.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Distribution (Probability theory); Insurance, Life > Mathematics; Probabilities; Annuities
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16260
• Institution: De La Salle University

This thesis is based on the paper entitled The Bounds of Bivariate Distributions that limit the value of last survivor annuities by Jacques F. Carriere and Lai K. Chan. The first two chapters are devoted to a review of basic probability concepts and actuarial mathematics concepts involving one life. Chapter three is a discussion on multiple life functions, specifically, the joint-life and last-survivor statuses. Chapter four is a detailed discussion of the above mentioned paper which is primarily on the effects of the dependence assumption on actuarial calculations.In this paper, we showed the effects on some actuarial functions namely axy which is the immediate annuity payable until the first death, and axy which is hte immediate annuity payable until the second death given different measures of association which are defined to be p = -1, p= 0, and p = 1. In relation to this a general bivariate model as well as its properties are discussed thoroughly. Moreover, a discussion on mixtures of distributions with given properties is also incorporated in this paper. This includes a special case of this class of distributions that is used for a simplified computation of probability and annuity functions. In addition to this, the change in the interest assumption that would give an annuity value equal to the change in the correlation from p = 0 to p = -1 or p = 1 are examined.