Document Type : Original Research Paper

Authors

• Z. Shojaee Azar ¹
• A. Hassan Zadeh ²

¹ Department of Actuarial Sciences, Allameh Tabatabai University, Tehran, Iran

² Department of Actuarial Sciences, Shahid Beheshti University, Tehran, Iran

Abstract

In this article, the application of phase-type distributions in the modeling of mortality rates has been investigated. Phase-type random variable is defined as the time to absorption moment (end point) in continuous Markov chains. In this article, instead of real age, we have used physiological age, which is defined as a health index. This age is determined according to the tissues and organs of the person's body. Each position of the Markov chain is considered a physiological age, and the end point of this chain determines the death of a person, then using the analytical method in the phase-type concept, we calculate all the probabilities related to death at the actual age. After modeling, we estimate the parameters of phase-type distribution by the least squared error method and then we fit the model to Iran's life table. Finally, by using these parameters and making sure that the model fits well to Iran's mortality table, we calculate finite closed expressions for the current value of whole life insurance and life annuity.

Keywords

• Phase-type Distribution
• Mortality Modeling
• Annuity Pricing
• Aging Process
• Physiological Age