IDEAS home Printed from https://ideas.repec.org/a/sgh/annals/i31y2013p101-116.html
   My bibliography  Save this article

Przestrzeń stanów i filtr Kalmana w teorii ubezpieczeń

Author

Listed:
  • Helena Jasiulewicz

    (Uniwersytet Przyrodniczy we Wrocławiu)

Abstract

W pracy przedstawiono elastyczne narzędzie służące do wyznaczania optymalnych estymatorów i predyktorów, jakim jest filtr Kalmana. Skupiono się na klasycznym algorytmie Kalmana związanym z liniową przestrzenią stanów zakłócanych szumem gaussowskim. Następnie przedstawiono zastosowanie filtru Kalmana do optymalnego prognozowania przyszłych rezerw szkodowych. Podano przykład wskazujący zalety filtru Kalmana w porównaniu z tradycyjnymi technikami typu chain-ladder wyznaczania rezerw szkodowych.

Suggested Citation

  • Helena Jasiulewicz, 2013. "Przestrzeń stanów i filtr Kalmana w teorii ubezpieczeń," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 101-116.
    • Handle: RePEc:sgh:annals:i:31:y:2013:p:101-116
    as

    Download full text from publisher

    File URL: http://rocznikikae.sgh.waw.pl/p/roczniki_kae_z31_06.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Atherino, Rodrigo & Pizzinga, Adrian & Fernandes, Cristiano, 2010. "A Row-Wise Stacking of the Runoff Triangle: State Space Alternatives for IBNR Reserve Prediction," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 917-946, November.
    2. Zehnwirth, Ben, 1985. "Linear Filtering and Recursive Credibility Estimation," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 19-35, April.
    3. Kremer, Erhard, 1994. "Robust Credibility via Robust Kalman Filtering," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 221-233, November.
    4. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    5. Piet de Jong, 2006. "Forecasting Runoff Triangles," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 28-38.
    6. de Jong, Piet & Zehnwirth, Ben, 1983. "Credibility theory and the Kalman filter," Insurance: Mathematics and Economics, Elsevier, vol. 2(4), pages 281-286, October.
    7. Ledolter, Johannes & Klugman, Stuart & Lee, Chang-Soo, 1991. "Credibility Models with Time-Varying Trend Components," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 73-91, April.
    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. Nataliya Chukhrova & Arne Johannssen, 2017. "State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing," Risks, MDPI, vol. 5(2), pages 1-23, May.
    2. Nataliya Chukhrova & Arne Johannssen, 2021. "Stochastic Claims Reserving Methods with State Space Representations: A Review," Risks, MDPI, vol. 9(11), pages 1-55, November.
    3. Leonardo Costa & Adrian Pizzinga, 2020. "State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 438-448, April.
    4. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    5. Portugal, Luís & Pantelous, Athanasios A. & Verrall, Richard, 2021. "Univariate and multivariate claims reserving with Generalized Link Ratios," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 57-67.
    6. Nataliya Chukhrova & Arne Johannssen, 2021. "Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving," Risks, MDPI, vol. 9(6), pages 1-5, June.
    7. de Alba, Enrique & Nieto-Barajas, Luis E., 2008. "Claims reserving: A correlated Bayesian model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 368-376, December.
    8. Cadogan, Godfrey, 2010. "Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance," MPRA Paper 23235, University Library of Munich, Germany.
    9. Pitselis, Georgios, 2004. "A seemingly unrelated regression model in a credibility framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 37-54, February.
    10. Adrian Pizzinga & Marcelo Fernandes, 2021. "Extensions to the invariance property of maximum likelihood estimation for affine‐transformed state‐space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 355-371, May.
    11. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    12. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Papers 1806.05939, arXiv.org.
    13. Álvarez-Jareño, José Antonio & Coll-Serrano, Vicente, 2012. "Estimación de reservas en una compañía aseguradora. Una aplicación en Excel del método Chain-Ladder y Bootstrap || Estimating the Reserves in Insurance Companies: An Excel Application of the Chain-Lad," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 14(1), pages 124-136, December.
    14. Doray, Louis G., 1996. "UMVUE of the IBNR reserve in a lognormal linear regression model," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 43-57, May.
    15. Bohnert, Alexander & Gatzert, Nadine & Kolb, Andreas, 2016. "Assessing inflation risk in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 86-96.
    16. Stephens, David A. & Crowder, Martin J. & Dellaportas, Petros, 2004. "Quantification of automobile insurance liability: a Bayesian failure time approach," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 1-21, February.
    17. Garrido, José & Romera, Rosario, 1995. "On credibility and robustness with the Kalman filter," DES - Working Papers. Statistics and Econometrics. WS 4509, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.
    19. Boj del Val, Eva & Costa Cor, Teresa, 2017. "Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year," Cuadernos de Gestión, Universidad del País Vasco - Instituto de Economía Aplicada a la Empresa (IEAE).
    20. Verrall, R.J. & England, P.D., 2005. "Incorporating expert opinion into a stochastic model for the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 355-370, October.

    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:101-116. 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.