IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i3p75-d160853.html
   My bibliography  Save this article

One-Year Change Methodologies for Fixed-Sum Insurance Contracts

Author

Listed:
  • Michel Dacorogna

    (Prime Re Solutions, 6340 Zug, Switzerland)

  • Alessandro Ferriero

    (Department of Mathematics, UAM, Campus de Cantoblanco, 28049 Madrid, Spain
    SCOR, General Guisan-Quai 26, 8022 Zurich, Switzerland)

  • David Krief

    (LPSM, Université Paris Diderot, 75013 Paris, France)

Abstract

We study the dynamics of the one-year change in P&C insurance reserves estimation by analyzing the process that leads to the ultimate risk in the case of “fixed-sum” insurance contracts. The random variable ultimately is supposed to follow a binomial distribution. We compute explicitly various quantities of interest, in particular the Solvency Capital Requirement for one year change and the Risk Margin, using the characteristics of the underlying model. We then compare them with the same figures calculated with existing risk estimation methods. In particular, our study shows that standard methods (Merz–Wüthrich) can lead to materially incorrect results if the assumptions are not fulfilled. This is due to a multiplicative error assumption behind the standard methods, whereas our example has an additive error propagation as often happens in practice.

Suggested Citation

  • Michel Dacorogna & Alessandro Ferriero & David Krief, 2018. "One-Year Change Methodologies for Fixed-Sum Insurance Contracts," Risks, MDPI, vol. 6(3), pages 1-29, July.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:75-:d:160853
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/3/75/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/6/3/75/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Busse, Marc & Müller, Ulrich & Dacorogna, Michel, 2010. "Robust Estimation of Reserve Risk," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 453-489, November.
    2. Ferriero, A., 2016. "Solvency capital estimation, reserving cycle and ultimate risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 162-168.
    3. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    4. Mack, Thomas, 2008. "Correction Note to “The Prediction Error of Bornhuetter/Ferguson” By T. Mack," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 669-669, November.
    5. Mack, Thomas, 2008. "The Prediction Error of Bornhuetter/Ferguson," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 87-103, May.
    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. Carnevale Giulio Ercole & Clemente Gian Paolo, 2020. "A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder," Risks, MDPI, vol. 8(4), pages 1-20, November.
    2. Michel Dacorogna, 2023. "How to Gain Confidence in the Results of Internal Risk Models? Approaches and Techniques for Validation," Risks, MDPI, vol. 11(5), pages 1-20, May.

    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. Dacorogna, Michel M, 2017. "Approaches and Techniques to Validate Internal Model Results," MPRA Paper 79632, University Library of Munich, Germany.
    2. Karthik Sriram & Peng Shi, 2021. "Stochastic loss reserving: A new perspective from a Dirichlet model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 195-230, March.
    3. 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.
    4. M. Hiabu & E. Mammen & M. D. Martìnez-Miranda & J. P. Nielsen, 2016. "In-sample forecasting with local linear survival densities," Biometrika, Biometrika Trust, vol. 103(4), pages 843-859.
    5. Michel Dacorogna, 2023. "How to Gain Confidence in the Results of Internal Risk Models? Approaches and Techniques for Validation," Risks, MDPI, vol. 11(5), pages 1-20, May.
    6. 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.
    7. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    8. 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.
    9. 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.
    10. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    11. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.
    12. Benjamin Avanzi & Yanfeng Li & Bernard Wong & Alan Xian, 2022. "Ensemble distributional forecasting for insurance loss reserving," Papers 2206.08541, arXiv.org, revised Feb 2024.
    13. Carnevale Giulio Ercole & Clemente Gian Paolo, 2020. "A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder," Risks, MDPI, vol. 8(4), pages 1-20, November.
    14. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    15. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2020. "Stochastic reserving with a stacked model based on a hybridized Artificial Neural Network," Papers 2008.07564, arXiv.org.
    16. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    17. Ferriero, A., 2016. "Solvency capital estimation, reserving cycle and ultimate risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 162-168.
    18. Oliver Stoner & Theo Economou, 2020. "Multivariate hierarchical frameworks for modeling delayed reporting in count data," Biometrics, The International Biometric Society, vol. 76(3), pages 789-798, September.
    19. Diers, Dorothea & Linde, Marc & Hahn, Lukas, 2016. "Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladde," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 187-199.
    20. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.

    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:gam:jrisks:v:6:y:2018:i:3:p:75-:d:160853. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.