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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
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    References listed on IDEAS

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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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