Predictive Mortality Graduation and the Value At Risk: A Bayesian Approach

M. Mendoza (ITAM, Mexico)

A.M. Madrigal (CNSF, Mexico)

and

E. Gutiérrez-Peña (IIMAS-UNAM, Mexico)

Abstract. Graduation and overestimation of death rates play a key role in the construction of mortality tables. The usual actuarial methods deal with each of these two aspects separately. Moreover, the statistical nature of these problems is typically ignored. In this paper, a method to produce mortality tables is proposed which simultaneously takes both issues into account. The approach is entirely statistical and allows the user to select a table providing a precisely defined level of protection against deviations in mortality. The problem is analyzed from a predictive perspective within the Bayesian framework and the solution makes use of the concept of value at risk.

Key words: Actuarial methods; Bayesian inference; mortality models; linear regression; predictive distribution; overestimation; value at risk.