Advertisement

European Actuarial Journal

, Volume 8, Supplement 1, pp 9–24 | Cite as

Solvency requirement for long term guarantee: risk measure versus probability of ruin

  • Pierre DevolderEmail author
Original Research Paper
  • 388 Downloads

Abstract

Solvency requirements are based on the idea that risk can be accepted if enough capital is present. The determination of this minimum level of capital depends on the way to consider and measure the underlying risk. Apart from the kind of risk measure used, an important factor is the way to integrate time in the process. This topic is particularly important for long term liabilities such as life insurance or pension benefits. In this paper we study the market risk of a life insurer offering a fixed guaranteed rate on a certain time horizon and investing the premium in a risky fund. We develop and compare various risk measurements based either on a single point analysis or on a continuous time test. Dynamic risk measures are also considered.

Keywords

Solvency capital Risk measure Probability of ruin Dynamic risk measure 

References

  1. 1.
    Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9:203–228MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Back K (2005) A course in derivatives securities. Springer, BerlinzbMATHGoogle Scholar
  3. 3.
    Bodie Z (1995) On the risks of stocks in the long run. Financ Anal J 51(3):68–76CrossRefGoogle Scholar
  4. 4.
    Bodie Z, Merton R, Samuelson P (1992) Labor supply flexibility and portfolio choice in a lifecycle model. J Econ Dyn Control 16(3):427–449Google Scholar
  5. 5.
    Briys E, de Varenne F (1997) On the risk of life insurance liabilities: debunking some common pitfalls. J Risk Insur 64(4):673–694CrossRefGoogle Scholar
  6. 6.
    Campbell J, Viceira L (2002) Strategic asset allocation—portfolio choice for long term investors. Oxford University Press, New YorkCrossRefGoogle Scholar
  7. 7.
    Emmer S, Kluppelberg C (2001) Optimal portfolios with bounded capital at risk. Math Financ 11(4):365–384MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Grosen A, Jorgensen P (2002) Life insurance liabilities at market value: an analysis of insolvency risk. Bonus policy and regulatory intervention rules in a barrier option framework. J Risk Insur 69(1):63–91CrossRefGoogle Scholar
  9. 9.
    Hardy M, Wirch JL (2004) The iterated CTE: a dynamic risk measure. North Am Actuar J 8:62–75MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lee W (1990) Diversification and time. Do investment horizons matter? J Portf Manag 4:60–69Google Scholar
  11. 11.
    McNeil A, Frey R, Embrechts P (2005) Quantitative risk management. Princeton, New JerseyzbMATHGoogle Scholar
  12. 12.
    Merton R (1992) Continuous time finance. Wiley, LondonzbMATHGoogle Scholar
  13. 13.
    Pflug G, Romisch W (2007) Modeling, measuring and managing risk. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  14. 14.
    Samuelson P (1994) The long term case for equities. J Portf Manag 21(1):15–24MathSciNetCrossRefGoogle Scholar
  15. 15.
    Samuelson P (1963) Risk and uncertainty: a fallacy of large numbers. Scientia 98:108–113Google Scholar
  16. 16.
    Sandstrom A (2006) Solvency. Chapman & Hall, LondonzbMATHGoogle Scholar
  17. 17.
    Thorley S (1995) The time diversification controversy. Financ Anal J 51(3):18–22CrossRefGoogle Scholar
  18. 18.
    Wirch JL, Hardy MR (1999) A synthesis of risk measures for capital adequacy. Insur Math Econ 25:337–347CrossRefzbMATHGoogle Scholar

Copyright information

© DAV / DGVFM 2011

Authors and Affiliations

  1. 1.Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)Université Catholique de Louvain (UCL)Louvain la NeuveBelgium

Personalised recommendations