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.
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References
Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9:203–228
Back K (2005) A course in derivatives securities. Springer, Berlin
Bodie Z (1995) On the risks of stocks in the long run. Financ Anal J 51(3):68–76
Bodie Z, Merton R, Samuelson P (1992) Labor supply flexibility and portfolio choice in a lifecycle model. J Econ Dyn Control 16(3):427–449
Briys E, de Varenne F (1997) On the risk of life insurance liabilities: debunking some common pitfalls. J Risk Insur 64(4):673–694
Campbell J, Viceira L (2002) Strategic asset allocation—portfolio choice for long term investors. Oxford University Press, New York
Emmer S, Kluppelberg C (2001) Optimal portfolios with bounded capital at risk. Math Financ 11(4):365–384
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):63–91
Hardy M, Wirch JL (2004) The iterated CTE: a dynamic risk measure. North Am Actuar J 8:62–75
Lee W (1990) Diversification and time. Do investment horizons matter? J Portf Manag 4:60–69
McNeil A, Frey R, Embrechts P (2005) Quantitative risk management. Princeton, New Jersey
Merton R (1992) Continuous time finance. Wiley, London
Pflug G, Romisch W (2007) Modeling, measuring and managing risk. World Scientific, Singapore
Samuelson P (1994) The long term case for equities. J Portf Manag 21(1):15–24
Samuelson P (1963) Risk and uncertainty: a fallacy of large numbers. Scientia 98:108–113
Sandstrom A (2006) Solvency. Chapman & Hall, London
Thorley S (1995) The time diversification controversy. Financ Anal J 51(3):18–22
Wirch JL, Hardy MR (1999) A synthesis of risk measures for capital adequacy. Insur Math Econ 25:337–347
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The revised version of the article can be found under doi:10.1007/s13385-011-0042-0 and is published in Eur. Actuar. J. (2011) 1:199–214.
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Devolder, P. Solvency requirement for long term guarantee: risk measure versus probability of ruin. Eur. Actuar. J. 8 (Suppl 1), 9–24 (2018). https://doi.org/10.1007/s13385-011-0036-y
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DOI: https://doi.org/10.1007/s13385-011-0036-y