[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i3p382-391.html
   My bibliography  Save this article

Bounds for some general sums of random variables

Author

Listed:
  • Landsman, Zinoviy
  • Vanduffel, Steven
Abstract
Rogers and Shi (1995) have used the technique of conditional expectations to derive approximations for the distribution of a sum of lognormals. In this paper we extend their results to more general sums of random variables. In particular we study sums of functions of dependent random variables that are multivariate normally distributed and also derive results for sums of functions of dependent random variables from the additive exponential dispersion family. The usefulness of our results for practical applications is also discussed.

Suggested Citation

  • Landsman, Zinoviy & Vanduffel, Steven, 2011. "Bounds for some general sums of random variables," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 382-391, March.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:382-391
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00337-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    2. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    3. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    4. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    5. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    6. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 145-161, June.
    7. Landsman, Zinoviy & Valdez, Emiliano A., 2005. "Tail Conditional Expectations for Exponential Dispersion Models," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 189-209, May.
    8. Bruce L. Jones & Ricardas Zitikis, 2005. "Testing for the order of risk measures: an application of L-statistics in actuarial science," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 193-211.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
    2. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
    3. 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.
    4. Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
    5. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2015. "Comonotonic Monte Carlo and its applications in option pricing and quantification of risk," Documents de travail du Centre d'Economie de la Sorbonne 15015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    7. Robert, Christian Y. & Therond, Pierre-E., 2014. "Distortion Risk Measures, Ambiguity Aversion And Optimal Effort," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 277-302, May.
    8. Antonella Campana & Paola Ferretti, 2008. "Bounds for Concave Distortion Risk Measures for Sums of Risks," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 43-51, Springer.
    9. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    10. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586, arXiv.org, revised Mar 2016.
    11. Christian Gourieroux & Wei Liu, 2006. "Efficient Portfolio Analysis Using Distortion Risk Measures," Working Papers 2006-17, Center for Research in Economics and Statistics.
    12. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    13. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
    14. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    15. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    16. Psarrakos, Georgios & Vliora, Polyxeni, 2021. "Sensitivity analysis and tail variability for the Wang’s actuarial index," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 147-152.
    17. Darolles, Serge & Gourieroux, Christian & Jasiak, Joann, 2009. "L-performance with an application to hedge funds," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 671-685, September.
    18. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    19. Jones, Bruce L. & Puri, Madan L. & Zitikis, Ricardas, 2006. "Testing hypotheses about the equality of several risk measure values with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 253-270, April.
    20. Yang, Jianping & Hu, Taizhong, 2016. "New developments on the Lp-metric between a probability distribution and its distortion," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 236-243.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:382-391. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.