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Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework

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  • Andreas Niemeyer

    (Institut für Versicherungswissenschaften, Universität Ulm, D-89069 Ulm, Germany)

Abstract

Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in practice typically chosen as time-constant percentages on top of the best estimate transition intensities. We develop a risk-oriented method for the allocation of a total safety margin to the single safety margins at each point in time and each state. In a case study, we demonstrate the suitability of the proposed method in different frameworks. The results show that the traditional method yields an unwanted variability of the safety level with respect to time, whereas the variability can be significantly reduced by the new method. Furthermore, the case study supports the German 60 percent rule for the technical interest rate.

Suggested Citation

  • Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:1:p:35-60:d:44878
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    References listed on IDEAS

    as
    1. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    2. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    3. Christiansen, Marcus C. & Denuit, Michel M. & Lazar, Dorina, 2012. "The Solvency II square-root formula for systematic biometric risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 257-265.
    4. Christiansen, Marcus C. & Steffensen, Mogens, 2013. "Safe-Side Scenarios For Financial And Biometrical Risk," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 323-357, September.
    5. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    6. Kevin Dowd & David Blake & Andrew Cairns, 2011. "A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 237-247.
    7. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    8. Christiansen, Marcus C. & Niemeyer, Andreas & Teigiszerová, Lucia, 2015. "Modeling and forecasting duration-dependent mortality rates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 65-81.
    9. Christiansen, Marcus C. & Denuit, Michel & Lazar, Dorina, 2012. "The Solvency II square-root formula for systematic biometric risk," LIDAM Reprints ISBA 2012002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
    11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
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