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

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  • Grzegorz Darkiewicz
  • Griselda Deelstra
  • Jan Dhaene
  • Tom Hoedemakers
  • Michèle Vanmaele

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

  • Grzegorz Darkiewicz & Griselda Deelstra & Jan Dhaene & Tom Hoedemakers & Michèle Vanmaele, 2009. "Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 847-866, December.
    • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:4:p:847-866
    DOI: 10.1111/j.1539-6975.2009.01322.x
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    References listed on IDEAS

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    Cited by:

    1. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    2. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 767-800, December.

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