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Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data

Author

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  • Marcin Szatkowski

    (SGH Warsaw School of Economics, Institute of Econometrics
    STU ERGO Hestia SA, Risk Department)

Abstract

In this work, we perform an analysis of the characteristics of the one-year andultimate reserve risk distributions commonly used in actuarial science: duration, first development factor, coefficient of variation, skewness coefficient, skewness-to-CoV ratio, emergence factor, emergence pattern, and risk margin run-off patterns. Our study is based on empirical data for two European markets: the Polish and Slovak markets. We provide benchmarks and ranges for the considered characteristics, as well as analyse the relations between them. We study Solvency II lines of business and compare our coefficients of variation to the Standard Formula reserve risk standard deviations. We investigate more deeply the topic of emergence pattern and risk margin run-off patterns.

Suggested Citation

  • Marcin Szatkowski, 2022. "Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 14(4), pages 225-262, December.
    • Handle: RePEc:psc:journl:v:14:y:2022:i:4:p:381-413
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    References listed on IDEAS

    as
    1. Buchwalder, Markus & Bühlmann, Hans & Merz, Michael & Wüthrich, Mario V., 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 521-542, November.
    2. 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.
    3. Buchwalder, Markus & Bühlmann, Hans & Merz, Michael & Wüthrich, Mario V., 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method – Final Remark," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 553-553, November.
    4. Gisler, Alois, 2019. "The Reserve Uncertainties In The Chain Ladder Model Of Mack Revisited," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 787-821, September.
    5. England, P.D. & Verrall, R.J. & Wüthrich, M.V., 2019. "On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 74-88.
    6. Ohlsson, Esbjörn & Lauzeningks, Jan, 2009. "The one-year non-life insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 203-208, October.
    7. Marcin Szatkowski & Łukasz Delong, 2021. "One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model," Risks, MDPI, vol. 9(9), pages 1-29, August.
    8. Moro, Eric Dal & Krvavych, Yuriy, 2017. "Probability Of Sufficiency Of Solvency Ii Reserve Risk Margins: Practical Approximations," ASTIN Bulletin, Cambridge University Press, vol. 47(3), pages 737-785, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    one-year risk; ultimate risk; reserve risk; emergence pattern; risk margin run-off pattern;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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