Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables

20 Pages Posted: 9 Nov 2009

See all articles by Grzegorz Darkiewicz

Grzegorz Darkiewicz

KU Leuven - Faculty of Business and Economics (FEB)

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Jan Dhaene

Katholieke Universiteit Leuven

Tom Hoedemakers

KU Leuven - Faculty of Business and Economics (FEB)

Michèle Vanmaele

Ghent University - Department of Applied Mathematics, Computer Science and Statistics

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.

Suggested Citation

Darkiewicz, Grzegorz and Deelstra, Griselda and Dhaene, Jan and Hoedemakers, Tom and Vanmaele, Michèle, Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables. Journal of Risk and Insurance, Vol. 76, Issue 4, pp. 847-866, December 2009, Available at SSRN: https://ssrn.com/abstract=1501380 or http://dx.doi.org/10.1111/j.1539-6975.2009.01322.x

Grzegorz Darkiewicz (Contact Author)

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Griselda Deelstra

Université Libre de Bruxelles (ULB) ( email )

Boulevard du Triomphe, CP210
Brussels, Brussels 1050
Belgium

Jan Dhaene

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Tom Hoedemakers

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Michèle Vanmaele

Ghent University - Department of Applied Mathematics, Computer Science and Statistics ( email )

Krijgslaan 281
Ghent, B-9000
Belgium

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