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Open AccessFeature PaperArticle

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

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Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Street, London, ON N6A 5B7, Canada
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risklab GmbH, Allianz Global Investors, Seidlstraße 24-24a, 80335 Munich, Germany
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Chair of Mathematical Finance, Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany
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Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
*
Author to whom correspondence should be addressed.
Academic Editor: Pavel Shevchenko
Risks 2016, 4(4), 41; https://doi.org/10.3390/risks4040041
Received: 5 September 2016 / Revised: 28 October 2016 / Accepted: 1 November 2016 / Published: 8 November 2016
(This article belongs to the Special Issue Ageing Population Risks)
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. View Full-Text
Keywords: variable annuities; surrender behavior; closed-form approximation; pricing; affine linear model variable annuities; surrender behavior; closed-form approximation; pricing; affine linear model
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Escobar, M.; Krayzler, M.; Ramsauer, F.; Saunders, D.; Zagst, R. Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs. Risks 2016, 4, 41.

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