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SAFE-SIDE SCENARIOS FOR FINANCIAL AND BIOMETRICAL RISK

  • Marcus C. Christiansen (a1) and Mogens Steffensen (a2)
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.

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Corresponding author
E-mail: marcus.christiansen@uni-ulm.de
References
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[1]Alexander, C. and Sheedy, E. (2008) Developing a stress testing framework based on market risk models. Journal of Banking and Finance, 32, 22202236.
[2]Aragons, J., Blanco, C. and Dowd, K. (2001) Incorporating stress tests into market risk modelling. Derivatives Quarterly, 7, 4449.
[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.
[4]Berkowitz, J. (2000) A coherent framework for stress testing. Journal of Risk, 2, 111.
[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.
[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), 79113.
[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, 680690.
[8]Christiansen, M.C. (2010) Biometric worst-case scenarios for multi-state life insurance policies. Insurance: Mathematics and Economics, 47, 190197.
[9]Christiansen, M.C. (2011) Making use of netting effects when composing life insurance contracts. European Actuarial Journal, 1(Suppl. 1), 4760.
[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), 587614.
[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, 257265.
[12]De Giovanni, D. (2010) Lapse rate modeling: A rational expectation approach. Scandinavian Actuarial Journal, 2010 (1), 5667.
[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.
[14]Fabozzi, F.J. (2005) The Handbook of Fixed Income Securities, 7th ed.New York: McGraw Hill.
[15]European Commission (2010) Fifth Quantitative Impact Study: Technical Specifications.
[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, 143145.
[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, 380392.
[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. 171202. Helsinki, Finland: ICA.
[19]Kaas, R., Laeven, R. and Nelsen, R. (2009) Worst VaR scenarios with given marginals and measures of association. Insurance: Mathematics and Economics, 44, 146158.
[20]Kupiec, P. (1998) Stress testing in a value at risk framework. Journal of Derivatives, 6, 724.
[21]Laeven, R. (2009) Worst VaR scenarios. Insurance: Mathematics and Economics, 44, 159163.
[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.1725769
[23]Li, J. and Szimayer, A. (2011) The uncertain force of mortality framework: Pricing unit-linked life insurance contracts. Insurance: Mathematics and Economics, 49, 471486.
[24]McNeil, A.J. and Smith, A.D. (2012) Multivariate stress scenarios and solvency. Insurance: Mathematics and Economics, 50, 299308.
[25]Milbrodt, H. and Stracke, A. (1997) Markov models and Thiele's integral equations for the prospective reserve. Insurance: Mathematics and Economics, 19, 187235.
[26]Norberg, R. (1999) A theory of bonus in life insurance. Finance and Stochastics, 3, 373390.
[27]Studer, G. (1997) Maximum Loss for Measurement of Market Risk, PhD thesis, ETH Zurich.
[28]Studer, G. (1999) Market risk computation for nonlinear portfolios. Journal of Risk, 1, 3353.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
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