Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables |
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| Authors: | Grzegorz Darkiewicz Griselda Deelstra† Jan Dhaene Tom Hoedemakers‡ Michèle Vanmaele§ |
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| Institution: | Grzegorz Darkiewicz and Jan Dhaene are in the Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium. Jan Dhaene can be contacted via e-mail:;. Griselda Deelstra is in the Department of Mathematics, ECARES and Solvay Business School, UniversitéLibre de Bruxelles, Boulevard du Triomphe 2, CP 210, 1050 Brussels, Belgium;. Tom Hoedemakers is at the University Center of Statistics, W. de Croylaan 54, 3001 Heverlee, Belgium;. Michèle Vanmaele is in the Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium. |
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| Abstract: | We investigate lower and upper bounds for right tails (stop-loss premiums) of deterministic and stochastic sums of nonindependent random variables. The bounds are derived using the concepts of comonotonicity, convex order, and conditioning. The performance of the presented approximations is investigated numerically for individual life annuity contracts as well as for life annuity portfolios, where mortality is modeled by Makeham's law, whereas investment returns are modeled by a Brownian motion process. |
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