IDEAS home Printed from https://ideas.repec.org/p/wuu/wpaper/hsc0701.html
   My bibliography  Save this paper

Asymptotic behavior of the finite time ruin probability of a gamma Levy process

Author

Listed:
  • Zbigniew Michna
  • Aleksander Weron

Abstract

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

Suggested Citation

  • Zbigniew Michna & Aleksander Weron, 2007. "Asymptotic behavior of the finite time ruin probability of a gamma Levy process," HSC Research Reports HSC/07/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    • Handle: RePEc:wuu:wpaper:hsc0701
    as

    Download full text from publisher

    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_07_01.pdf
    File Function: Final draft, 2006
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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, 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. 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.
    2. 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).
    3. 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.
    4. repec:hum:wpaper:sfb649dp2006-010 is not listed on IDEAS
    5. 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.
    6. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    7. Borak, Szymon & Fengler, Matthias R. & Härdle, Wolfgang Karl, 2005. "DSFM fitting of implied volatility surfaces," SFB 649 Discussion Papers 2005-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    9. Detlefsen, Kai & Härdle, Wolfgang Karl & Moro, Rouslan A., 2007. "Empirical pricing kernels and investor preferences," SFB 649 Discussion Papers 2007-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. repec:hum:wpaper:sfb649dp2005-016 is not listed on IDEAS
    11. 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.
    12. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    13. 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.
    14. Härdle, Wolfgang Karl & Klinke, Sigbert & Ziegenhagen, Uwe, 2006. "E-learning statistics: A selective review," SFB 649 Discussion Papers 2006-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    16. 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.
    17. Joanna Janczura & Rafal Weron, 2011. "Black swans or dragon kings? A simple test for deviations from the power law," Papers 1102.3712, arXiv.org.
    18. 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.
    19. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    20. Marcin Rudź, 2015. "A method of calculating exact ruin probabilities in discrete time models," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 307-322.
    21. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    22. Chen, Ying & Härdle, Wolfgang Karl & Spokoiny, Vladimir, 2006. "GHICA: Risk analysis with GH distributions and independent components," SFB 649 Discussion Papers 2006-078, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    More about this item

    Keywords

    Ruin probability; gamma Levy process; risk process;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:wuu:wpaper:hsc0701. 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: Rafal Weron (email available below). General contact details of provider: https://edirc.repec.org/data/hspwrpl.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.