Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection

Authors:
Michel Denuit;Jan Dhaene
Affiliations:
Institut des Sciences Actuarielles, Université Catholique de Louvain, Louvain-la-Neuve, Belgium;Catholic University of Leuven, Center for Risk and Insurance Studies, B-3000 Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In the Lee-Carter framework, future survival probabilities are random variables with an intricate distribution function. In large homogeneous portfolios of life annuities, value-at-risk or conditional tail expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities. This paper aims to derive some bounds in the increasing convex (or stop-loss) sense on these random survival probabilities. These bounds are obtained with the help of comonotonic upper and lower bounds on sums of correlated random variables.