IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i12p221-d1302518.html
   My bibliography  Save this article

Stochastic Chain-Ladder Reserving with Modeled General Inflation

Author

Listed:
  • Massimo De Felice

    (Department of Statistical Sciences, Sapienza University of Rome, 00185 Roma, Italy)

  • Franco Moriconi

    (Department of Economics, University of Perugia, 06123 Perugia, Italy)

Abstract

We consider two possible approaches to the problem of incorporating explicit general (i.e., economic) inflation in the non-life claims reserve estimates and the corresponding reserve SCR, defined—as in Solvency II—under the one-year view. What we call the actuarial approach provides a simplified solution to the problem, obtained under the assumption of deterministic interest rates and absence of inflation risk premia. The market approach seeks to eliminate these shortcomings by combining a stochastic claims reserving model with a stochastic market model for nominal and real interest rates. The problem is studied in details referring to the stochastic chain-ladder provided by the Over-dispersed Poisson model. The application of the two approaches is illustrated by a worked example based on market data.

Suggested Citation

  • Massimo De Felice & Franco Moriconi, 2023. "Stochastic Chain-Ladder Reserving with Modeled General Inflation," Risks, MDPI, vol. 11(12), pages 1-31, December.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:12:p:221-:d:1302518
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/12/221/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/11/12/221/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    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. Brydon, D. & Verrall, R. J., 2009. "Calendar Year Effects, Claims Inflation and the Chain-Ladder Technique," Annals of Actuarial Science, Cambridge University Press, vol. 4(2), pages 287-301, September.
    4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    5. Sara Cecchetti & Adriana Grasso & Marcello Pericoli, 2022. "An analysis of objective inflation expectations and inflation risk premia," Temi di discussione (Economic working papers) 1380, Bank of Italy, Economic Research and International Relations Area.
    6. Franco Moriconi, 2023. "A Three-Factor Market Model for Incorporating Explicit General Inflation in Non-Life Claims Reserving," Risks, MDPI, vol. 11(10), pages 1-32, October.
    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. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    2. 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.
    3. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    4. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    5. Tomas Björk & Magnus Blix & Camilla Landén, 2006. "On Finite Dimensional Realizations For The Term Structure Of Futures Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 281-314.
    6. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    7. Huse, Cristian, 2011. "Term structure modelling with observable state variables," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3240-3252.
    8. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    9. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    10. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    11. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
    12. Y. D'Halluin & P. A. Forsyth & K. R. Vetzal & G. Labahn, 2001. "A numerical PDE approach for pricing callable bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(1), pages 49-77.
    13. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
    14. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    15. Spiros H. Martzoukos & Theodore M. Barnhill Jr., 1998. "The Survival Zone For A Bond With Both Call And Put Options Embedded," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 21(4), pages 419-430, December.
    16. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    17. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    18. Giuseppe Orlando & Michele Bufalo, 2021. "Interest rates forecasting: Between Hull and White and the CIR#—How to make a single‐factor model work," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1566-1580, December.
    19. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    20. Luca Capriotti & Yupeng Jiang & Gaukhar Shaimerdenova, 2019. "Approximation Methods For Inhomogeneous Geometric Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-16, March.

    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:11:y:2023:i:12:p:221-:d:1302518. 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.