IDEAS home Printed from https://ideas.repec.org/a/prg/jnlpep/v2017y2017i5id625p542-560.html
   My bibliography  Save this article

Stochastic Claims Reserving in Insurance Using Random Effects

Author

Listed:
  • Michal Gerthofer
  • Michal Pešta

Abstract

Estimation of claims reserves, which should be held by the insurer so as to be able to meet expected future claims arising from policies currently in force and policies written in the past, presents an important task for insurance companies to predict their liabilities. A common approach to the reser-ving problem is based on generalized linear models (GLM). In this article, the application of genera-lized linear mixed models (GLMM) - an extension of the GLM - for estimation of the loss reserves is shown. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of risk management and capital allocation practices of non-life insurers. A real data example together with diagnostics for the model selection are provided as an illustration of the potential benefits of the presented approach.

Suggested Citation

  • Michal Gerthofer & Michal Pešta, 2017. "Stochastic Claims Reserving in Insurance Using Random Effects," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(5), pages 542-560.
    • Handle: RePEc:prg:jnlpep:v:2017:y:2017:i:5:id:625:p:542-560
    DOI: 10.18267/j.pep.625
    as

    Download full text from publisher

    File URL: http://pep.vse.cz/doi/10.18267/j.pep.625.html
    Download Restriction: free of charge
    File URL: http://pep.vse.cz/doi/10.18267/j.pep.625.pdf
    Download Restriction: free of charge
    File URL: https://libkey.io/10.18267/j.pep.625?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    2. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    3. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    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. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    2. Martin Hrba & Matúš Maciak & Barbora Peštová & Michal Pešta, 2022. "Bootstrapping Not Independent and Not Identically Distributed Data," Mathematics, MDPI, vol. 10(24), pages 1-26, December.

    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. Pitselis, Georgios & Grigoriadou, Vasiliki & Badounas, Ioannis, 2015. "Robust loss reserving in a log-linear model," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 14-27.
    2. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    3. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.
    4. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2017. "Reserve modelling and the aggregation of risks using time varying copula models," Economic Modelling, Elsevier, vol. 67(C), pages 149-158.
    5. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2018. "Dynamic and granular loss reserving with copulae," Papers 1801.01792, arXiv.org.
    6. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676, September.
    7. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    8. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    9. Hudecová, Šárka & Pešta, Michal, 2013. "Modeling dependencies in claims reserving with GEE," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 786-794.
    10. 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.
    11. de Andres-Sanchez, Jorge, 2007. "Claim reserving with fuzzy regression and Taylor's geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 145-163, January.
    12. Lars Hougaard Hansen & Bent Nielsen & Jens Perch Nielsen, 2004. "Two sided analysis of variance with a latent time series," Economics Papers 2004-W25, Economics Group, Nuffield College, University of Oxford.
    13. COSTA, JUAN IGNACIO BACCINO & DE ARMAS, GONZALO & Álvarez-Vaz, Ramón Dr., 2022. "Estudio De Algunos Métodos De Reservas Técnicas En Condiciones De Incertidumbre Para Seguros De No Vida (Study Of Some Methods Of Technical Reserves Under Conditions Of Uncertainty For Non-Life Insura," OSF Preprints 3pjr9, Center for Open Science.
    14. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    15. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    16. Shengkun Xie & Chong Gan, 2023. "Estimating Territory Risk Relativity Using Generalized Linear Mixed Models and Fuzzy C -Means Clustering," Risks, MDPI, vol. 11(6), pages 1-20, May.
    17. Gian Paolo Clemente & Nino Savelli & Diego Zappa, 2019. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance," International Business Research, Canadian Center of Science and Education, vol. 12(3), pages 123-138, March.
    18. Martin Hrba & Matúš Maciak & Barbora Peštová & Michal Pešta, 2022. "Bootstrapping Not Independent and Not Identically Distributed Data," Mathematics, MDPI, vol. 10(24), pages 1-26, December.
    19. Crevecoeur, Jonas & Antonio, Katrien & Verbelen, Roel, 2019. "Modeling the number of hidden events subject to observation delay," European Journal of Operational Research, Elsevier, vol. 277(3), pages 930-944.
    20. Corneliu Cristian Bente, 2017. "Actuarial Estimation Of Technical Reserves In Insurance Companies. Basic Chain Ladder Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 227-234, July.

    More about this item

    Keywords

    claims reserving; non-life insurance; dependency modelling; random effects; mixed models; GLM; GLMM; panel data;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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:prg:jnlpep:v:2017:y:2017:i:5:id:625:p:542-560. 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: Stanislav Vojir (email available below). General contact details of provider: https://edirc.repec.org/data/uevsecz.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.