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Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs

Listed author(s):
  • Marcos Escobar


    (Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Street, London, ON N6A 5B7, Canada)

  • Mikhail Krayzler


    (risklab GmbH, Allianz Global Investors, Seidlstraße 24-24a, 80335 Munich, Germany)

  • Franz Ramsauer


    (Chair of Mathematical Finance, Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany)

  • David Saunders


    (Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada)

  • Rudi Zagst


    (Chair of Mathematical Finance, Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany)

Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities with guaranteed minimum repayments at maturity and in case of the insured’s death. If the contract is prematurely surrendered, the policyholder is entitled to the current value of the fund account reduced by the prevailing surrender fee. The financial market and the mortality model are affine linear. For the surrender model, a Cox process is deployed whose intensity is given by a deterministic function (s-curve) with stochastic inputs from the financial market. So, the policyholders’ surrender behavior depends on the performance of the financial market and is stochastic. The presented pricing scheme incorporates the stochastic surrender behavior of the policyholders and is only based on suitable closed-form approximations.

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Article provided by MDPI, Open Access Journal in its journal Risks.

Volume (Year): 4 (2016)
Issue (Month): 4 (November)
Pages: 1-36

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Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:41-:d:82367
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  15. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
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  17. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  18. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-31, July.
  19. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
  20. Kling, Alexander & Ruez, Frederik & Ruß, Jochen, 2011. "The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(02), pages 511-545, November.
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