IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-88-470-0704-8_6.html
   My bibliography  Save this book chapter

Bounds for Concave Distortion Risk Measures for Sums of Risks

In: Mathematical and Statistical Methods in Insurance and Finance

Author

Listed:
  • Antonella Campana

    (University of Molise)

  • Paola Ferretti

    (University of Venice)

Abstract

In this paper we consider the problem of studying the gap between bounds of risk measures of sums of non-independentrandom variables. Owing to the choice of the context of where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure of a discrete risk by referring to its writing as sum of layers. Then, we examine the case of sums of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. Finally, the attention is devoted to the analysis of the gap between risk measures of upper and lower bounds, with the aim of optimizing it.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sprchp:978-88-470-0704-8_6
    DOI: 10.1007/978-88-470-0704-8_6
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    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. 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.
    4. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    5. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    6. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    7. Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
    8. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    Full references (including those not matched with items on IDEAS)

    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. Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
    2. 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.
    3. Antonella Campana, 2007. "On Tail Value-at-Risk for sums of non-independent random variables with a generalized Pareto distribution," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(2), pages 169-180, December.
    4. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.
    5. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    6. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    7. Jae Youn Ahn, 2015. "Negative Dependence Concept in Copulas and the Marginal Free Herd Behavior Index," Papers 1503.03180, arXiv.org.
    8. Daniël Linders & Jan Dhaene & Wim Schoutens, 2015. "Option prices and model-free measurement of implied herd behavior in stock markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-35.
    9. J. Marin-Solano (Universitat de Barcelona) & O. Roch (Universitat de Barcelona) & J. Dhaene (Katholieke Univerisiteit Leuven) & C. Ribas (Universitat de Barcelona) & M. Bosch-Princep (Universitat de B, 2009. "Buy-and-Hold Strategies and Comonotonic Approximations," Working Papers in Economics 213, Universitat de Barcelona. Espai de Recerca en Economia.
    10. Mierzejewski, Fernando, 2007. "The Short-Run Monetary Equilibrium with Liquidity Constraints," MPRA Paper 6526, University Library of Munich, Germany.
    11. Chuancun Yin & Dan Zhu, 2016. "Sharp convex bounds on the aggregate sums--An alternative proof," Papers 1603.05373, arXiv.org, revised May 2016.
    12. 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.
    13. Bahareh Afhami & Mohsen Rezapour & Mohsen Madadi & Vahed Maroufy, 2021. "Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk," Papers 2104.11594, arXiv.org.
    14. Brückner, Karsten, 2008. "Quantifying the error of convex order bounds for truncated first moments," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 261-270, February.
    15. Laeven, Roger J.A., 2009. "Worst VaR scenarios: A remark," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 159-163, April.
    16. Van Weert, Koen & Dhaene, Jan & Goovaerts, Marc, 2010. "Optimal portfolio selection for general provisioning and terminal wealth problems," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 90-97, August.
    17. Annaert, Jan & Deelstra, Griselda & Heyman, Dries & Vanmaele, Michèle, 2007. "Risk management of a bond portfolio using options," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 299-316, November.
    18. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
    19. 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.
    20. Karel in 't Hout & Jacob Snoeijer, 2021. "Numerical valuation of American basket options via partial differential complementarity problems," Papers 2106.01200, arXiv.org.

    More about this item

    Keywords

    Distortion risk measures; Discrete risks; Concave risk measures; Upper and lower bounds; Gap between bounds;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    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:spr:sprchp:978-88-470-0704-8_6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.