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SAFE-SIDE SCENARIOS FOR FINANCIAL AND BIOMETRICAL RISK

Published online by Cambridge University Press:  10 July 2013

Marcus C. Christiansen  and
Mogens Steffensen
Marcus C. Christiansen*
Affiliation:
Institut für Versicherungswissenschaften, Universität Ulm, D-89069 Ulm, Germany
Mogens Steffensen
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen, Denmark
*
E-mail: [email protected]
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Abstract

Premium settlement and calculation of reserves and capital requirements are typically based on worst- or just bad-case assumptions on interest rates, mortality rates, and other transition rates between states defined according to the insurance benefits. If interest and transition rates are chosen independently from each other, the worst choice, i.e. the combination of interest rates and transition rates that maximizes the reserve, can be found by dynamic programming. Here, we generalize this idea by choosing the interest and transition rates from a set that allows for mutual dependence. In general, finding the worst case is much more complicated in this situation, but we characterize a set of relatively tractable problems and present a series of examples from this set. Our approach with mutual dependence is relevant e.g. for internal models in Solvency II.

Keywords

Worst-case scenariosinterest and transition ratesdependencefirst-order basiscapital requirement
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 323 - 357
Copyright
Copyright © ASTIN Bulletin 2013 

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References

[1]Alexander, C. and Sheedy, E. (2008) Developing a stress testing framework based on market risk models. Journal of Banking and Finance, 32, 2220–2236.CrossRefGoogle Scholar
[2]Aragons, J., Blanco, C. and Dowd, K. (2001) Incorporating stress tests into market risk modelling. Derivatives Quarterly, 7, 44–49.Google Scholar
[3]Bauer, D., Bergmann, D. and Reuss, A. (2010) Solvency II and Nested Simulations – A Least-Squares Monte Carlo Approach. In Proceedings of the 2010 ICA Congress.Google Scholar
[4]Berkowitz, J. (2000) A coherent framework for stress testing. Journal of Risk, 2, 1–11.CrossRefGoogle Scholar
[5]Börger, M. (2010) Deterministic shock vs. stochastic value-at-risk: An analysis of the Solvency II standard model approach to longevity risk. Blätter der DGVFM, 225–259.Google Scholar
[6]Cairns, A.J.G., Blake, D. and Dowd, K. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2008 (2–3), 79–113.CrossRefGoogle Scholar
[7]Christiansen, M.C. (2008) A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension. Insurance: Mathematics and Economics, 42, 680–690.Google Scholar
[8]Christiansen, M.C. (2010) Biometric worst-case scenarios for multi-state life insurance policies. Insurance: Mathematics and Economics, 47, 190–197.Google Scholar
[9]Christiansen, M.C. (2011) Making use of netting effects when composing life insurance contracts. European Actuarial Journal, 1(Suppl. 1), 47–60.CrossRefGoogle Scholar
[10]Christiansen, M.C. and Denuit, M.M. (2010) First-order mortality rates and safe-side actuarial calculations in life insurance. ASTIN Bulletin, 40 (2), 587–614.Google Scholar
[11]Christiansen, M.C., Denuit, M.M. and Lazar, D. (2012) The Solvency II square-root formula for systematic biometric risk. Insurance: Mathematics and Economics, 50, 257–265.Google Scholar
[12]De Giovanni, D. (2010) Lapse rate modeling: A rational expectation approach. Scandinavian Actuarial Journal, 2010 (1), 56–67.CrossRefGoogle Scholar
[13]European Commission (2008) Directive of the European Parliament and of the Council on the taking-up and pursuit of the business of insurance and reinsurance. (Solvency II). COM(2008) 119.Google Scholar
[14]Fabozzi, F.J. (2005) The Handbook of Fixed Income Securities, 7th ed.New York: McGraw Hill.Google Scholar
[15]European Commission (2010) Fifth Quantitative Impact Study: Technical Specifications.Google Scholar
[16]Genest, C., Gerber, H.U., Goovaerts, M.J. and Laeven, R.J.A. (2009) Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance. Insurance: Mathematics and Economics, 44, 143–145.Google Scholar
[17]Goovaerts, M.J., Kaas, R. and Laeven, R.J.A. (2011) Worst case risk measurement: Back to the future? Insurance: Mathematics and Economics, 49, 380–392.Google Scholar
[18]Hoem, J.M. (1988) The versatility of the Markov chain as a tool in the mathematics of life insurance. In Transactions of the 23rd International Congress of Actuaries, Vol. 3, pp. 171–202. Helsinki, Finland: ICA.Google Scholar
[19]Kaas, R., Laeven, R. and Nelsen, R. (2009) Worst VaR scenarios with given marginals and measures of association. Insurance: Mathematics and Economics, 44, 146–158.Google Scholar
[20]Kupiec, P. (1998) Stress testing in a value at risk framework. Journal of Derivatives, 6, 7–24.CrossRefGoogle Scholar
[21]Laeven, R. (2009) Worst VaR scenarios. Insurance: Mathematics and Economics, 44, 159–163.Google Scholar
[22]Li, J. and Szimayer, A. (2010) The Effect of Policyholders Rationality on Unit-Linked Life Insurance Contracts with Surrender Guarantees (December 15, 2010). Available at SSRN: http://ssrn.com/abstract=1725769 or doi:10.2139/ssrn.1725769Google Scholar
[23]Li, J. and Szimayer, A. (2011) The uncertain force of mortality framework: Pricing unit-linked life insurance contracts. Insurance: Mathematics and Economics, 49, 471–486.Google Scholar
[24]McNeil, A.J. and Smith, A.D. (2012) Multivariate stress scenarios and solvency. Insurance: Mathematics and Economics, 50, 299–308.Google Scholar
[25]Milbrodt, H. and Stracke, A. (1997) Markov models and Thiele's integral equations for the prospective reserve. Insurance: Mathematics and Economics, 19, 187–235.Google Scholar
[26]Norberg, R. (1999) A theory of bonus in life insurance. Finance and Stochastics, 3, 373–390.CrossRefGoogle Scholar
[27]Studer, G. (1997) Maximum Loss for Measurement of Market Risk, PhD thesis, ETH Zurich.CrossRefGoogle Scholar
[28]Studer, G. (1999) Market risk computation for nonlinear portfolios. Journal of Risk, 1, 33–53.CrossRefGoogle Scholar