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Analytical calculation of risk measures for variable annuity guaranteed benefits

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  • Feng, Runhuan
  • Volkmer, Hans W.

Abstract

With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been observed to be time consuming and sometimes extremely costly. In this paper we propose alternative analytical methods for the calculation of risk measures for variable annuity guaranteed benefits on a stand-alone basis. The techniques for analytical calculations are based on the study of geometric Brownian motion and its integral. Another novelty of the paper is to propose a quantitative model which assesses both market risk on the liability side and revenue risk on the asset side in the same framework from the viewpoint of risk management. As we demonstrate by numerous examples on quantile risk measure and conditional tail expectation, the methods and numerical algorithms developed in this paper appear to be both accurate and computationally efficient.

Suggested Citation

  • Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:636-648
    DOI: 10.1016/j.insmatheco.2012.09.007
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. " Comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior," Working Papers Department of Accounting, Finance and Insurance (AFI) 485229, KU Leuven, Faculty of Economics and Business, Department of Accounting, Finance and Insurance (AFI).
    2. Dan Pirjol & Lingjiong Zhu, 2016. "Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options," Papers 1609.07558, arXiv.org.
    3. Feng, Runhuan & Huang, Huaxiong, 2016. "Statutory financial reporting for variable annuity guaranteed death benefits: Market practice, mathematical modeling and computation," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 54-64.
    4. Yoo Byoung Hark & Ko Bangwon & Kwon Hyuk-Sung, 2016. "On the Bayesian Risk Evaluation of Minimum Guarantees in Variable Annuities," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 10(1), pages 21-43, January.
    5. Pirjol, Dan & Zhu, Lingjiong, 2016. "Discrete sums of geometric Brownian motions, annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 19-37.
    6. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    7. Runhuan Feng & Alexey Kuznetsov & Fenghao Yang, 2016. "Exponential functionals of Levy processes and variable annuity guaranteed benefits," Papers 1610.00577, arXiv.org.
    8. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    9. Steinorth, Petra & Mitchell, Olivia S., 2015. "Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 246-258.
    10. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.

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