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The one-year non-life insurance risk

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  • Ohlsson, Esbjörn
  • Lauzeningks, Jan

Abstract

A major part of the literature on non-life insurance reserve risk has been devoted to the ultimo risk, the risk in the full run-off of the liabilities. This is in contrast to the short time horizon in internal risk models at insurance companies, and the one-year risk perspective taken in the Solvency II project of the European Community. This paper aims at clarifying the one-year risk concept and describing simulation approaches, in particular for the one-year reserve risk. We also discuss the one-year premium risk and its relation to the premium reserve. Finally, we initiate a discussion on the role of risk margins and discounting for the reserve and premium risk, with focus on the Cost-of-Capital method. We show that risk margins do not affect the reserve risk and show how reserve duration can be used for easy calculation of risk margins. 1

Suggested Citation

  • Ohlsson, Esbjörn & Lauzeningks, Jan, 2009. "The one-year non-life insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 203-208, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:203-208
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    References listed on IDEAS

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    1. 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.
    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. Schnieper, R., 1991. "Separating True IBNR and IBNER Claims1," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 111-127, April.
    4. Kaufmann, Roger & Gadmer, Andreas & Klett, Ralf, 2001. "Introduction to Dynamic Financial Analysis," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 213-249, May.
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    Cited by:

    1. Mathias Lindholm & Filip Lindskog & Felix Wahl, 2017. "Valuation of Non-Life Liabilities from Claims Triangles," Risks, MDPI, vol. 5(3), pages 1-28, July.
    2. Alessandro Ricotta & Edoardo Luini, 2019. "Bayesian Estimation of Structure Variables in the Collective Risk Model for Reserve Risk," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 9(2), pages 1-2.
    3. Robert, Christian Y., 2013. "Market Value Margin calculations under the Cost of Capital approach within a Bayesian chain ladder framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 216-229.
    4. Pauline Milaure Ngugnie Diffouo & Pierre Devolder, 2020. "Longevity Risk Measurement of Life Annuity Products," Risks, MDPI, vol. 8(1), pages 1-16, March.
    5. Antoine Mandel & Timothy Tiggeloven & Daniel Lincke & Elco Koks & Philip Ward & Jochen Hinkel, 2021. "Risks on global financial stability induced by climate change: the case of flood risks," Climatic Change, Springer, vol. 166(1), pages 1-24, May.
    6. Diers, Dorothea & Linde, Marc, 2013. "The multi-year non-life insurance risk in the additive loss reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 590-598.
    7. Happ, Sebastian & Merz, Michael & Wüthrich, Mario V., 2012. "Claims development result in the paid-incurred chain reserving method," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 66-72.
    8. 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.
    9. 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.
    10. Hahn, Lukas, 2017. "Multi-year non-life insurance risk of dependent lines of business in the multivariate additive loss reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 71-81.
    11. 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.
    12. Geoffrey Nichil & Pierre Vallois, 2019. "Solvency Need Resulting from Reserving Risk in a ORSA Context," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 567-592, June.
    13. Wahl, Felix, 2019. "Explicit moments for a class of micro-models in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 140-156.

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