IDEAS home Printed from https://ideas.repec.org/a/sgh/annals/i31y2013p137-155.html
   My bibliography  Save this article

Odporność składki kwantylowej ze względu na zaburzenia rozkładu wielkości pojedynczej szkody w modelu ryzyka łącznego

Author

Listed:
  • Arkadiusz Filip

    (Szkoła Główna Handlowa w Warszawie)

  • Marcin Wienke

    (Szkoła Główna Handlowa w Warszawie)

Abstract

Artykuł porusza problem kalkulacji składki przez zakład ubezpieczeń za pomocą metody kwantylowej przy zastosowaniu kolektywnego modelu ryzyka. W ustalonym modelu matematycznym wyliczenie składki wiąże się z błędami aproksymacji wynikającymi z zastosowania jednej z wielu dostępnych metod aproksymacji łącznego rozkładu szkód i zagadnieniem odporności składki na różnego rodzaju zaburzenia. W wyliczeniach uwzględniono możliwość popełnienia różnych błędów w procesie kalkulacji składki, wynikających z faktu, że zakład ubezpieczeń nie dysponuje pełną wiedzą o charakterystykach procesu szkodowego i jest zmuszony przyjmować o nim pewne założenia. Wrażliwość otrzymywanych wyników została zbadana ze względu na zmiany wielkości portfela ubezpieczeniowego, rozkładów prawdopodobieństwa używanych do modelowania wielkości pojedynczej szkody, metody aproksymacji, siły zaburzenia i rzędu kwantyla używanego do wyliczenia składki.

Suggested Citation

  • Arkadiusz Filip & Marcin Wienke, 2013. "Odporność składki kwantylowej ze względu na zaburzenia rozkładu wielkości pojedynczej szkody w modelu ryzyka łącznego," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 137-155.
    • Handle: RePEc:sgh:annals:i:31:y:2013:p:137-155
    as

    Download full text from publisher

    File URL: http://rocznikikae.sgh.waw.pl/p/roczniki_kae_z31_08.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Reijnen, Rajko & Albers, Willem & Kallenberg, Wilbert C.M., 2005. "Approximations for stop-loss reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 237-250, June.
    2. Ramsay, Colin M., 1991. "A Note of the Normal Power Approximation," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(01), pages 147-150, April.
    3. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
    4. Chaubey, Yogendra P. & Garrido, Jose & Trudeau, Sonia, 1998. "On the computation of aggregate claims distributions: some new approximations," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 215-230, December.
    5. Berger, Gottfried, 1972. "Integration of the normal power approximation," ASTIN Bulletin, Cambridge University Press, vol. 7(1), pages 90-95, December.
    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. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    2. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2023. "How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework," Sustainability, MDPI, vol. 15(9), pages 1-19, May.
    3. Sukono & Herlina Napitupulu & Riaman & Riza Andrian Ibrahim & Muhamad Deni Johansyah & Rizki Apriva Hidayana, 2023. "A Regional Catastrophe Bond Pricing Model and Its Application in Indonesia’s Provinces," Mathematics, MDPI, vol. 11(18), pages 1-20, September.
    4. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    5. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    6. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    7. Reijnen, Rajko & Albers, Willem & Kallenberg, Wilbert C.M., 2005. "Approximations for stop-loss reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 237-250, June.
    8. Michal Benko & Wolfgang Härdle & Alois Kneip, 2006. "Common Functional Principal Components," SFB 649 Discussion Papers SFB649DP2006-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    10. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    11. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2024. "Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength," Mathematics, MDPI, vol. 12(6), pages 1-21, March.
    12. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    13. Michal Benko & Alois Kneip, 2005. "Common functional component modelling," SFB 649 Discussion Papers SFB649DP2005-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Ogwang, Tomson, 2013. "Is the wealth of the world’s billionaires Paretian?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 757-762.
    15. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    16. Climent Hernández José Antonio & Venegas Martínez Francisco, 2013. "Valuación de opciones sobre subyacentes con rendimientos a-estables," Contaduría y Administración, Accounting and Management, vol. 58(4), pages 119-150, octubre-d.
    17. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    18. Wolfgang Karl Härdle & Brenda López Cabrera & Awdesch Melzer, 2021. "Pricing wind power futures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 1083-1102, August.
    19. Joanna Janczura & Rafal Weron, 2011. "Black swans or dragon kings? A simple test for deviations from the power law," Papers 1102.3712, arXiv.org.
    20. Ci­zek, P. & Tamine, J. & Härdle, W., 2008. "Smoothed L-estimation of regression function," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5154-5162, August.

    More about this item

    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:sgh:annals:i:31:y:2013:p:137-155. 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: Michał Bernardelli (email available below). General contact details of provider: https://edirc.repec.org/data/sgwawpl.html .

    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.