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Hedging Equity-Linked Life Insurance Contracts

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  • Thomas Møller

Abstract

This paper examines a portfolio of equity-linked life insurance contracts and determines risk-minimizing hedging strategies within a discrete-time setup. As a principal example, I consider the Cox-Ross-Rubinstein model and an equity-linked pure endowment contract under which the policyholder receives max(ST, K) at time T if he or she is then alive, where ST is the value of a stock index at the term T of the contract and K is a guarantee stipulated by the contract. In contrast to most of the existing literature, I view the contracts as contingent claims in an incomplete model and discuss the problem of choosing an optimality criterion for hedging strategies. The subsequent analysis leads to a comparison of the risk (measured by the variance of the insurer’s loss) inherent in equity-linked contracts in the two situations where the insurer applies the risk-minimizing strategy and the insurer does not hedge. The paper includes numerical results that can be used to quantify the effect of hedging and describe how this effect varies with the size of the insurance portfolio and assumptions concerning the mortality.

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  • Thomas Møller, 2001. "Hedging Equity-Linked Life Insurance Contracts," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 79-95.
    • Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:79-95
    DOI: 10.1080/10920277.2001.10595986
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    Cited by:

    1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    2. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    3. Мельников А.В. & Молибога М.М., 2003. "Расчеты Схем Гибкого Страхования," Higher School of Economics Economic Journal Экономический журнал Высшей школы экономики, CyberLeninka;Федеральное государственное автономное образовательное учреждение высшего образования «Национальный исследовательский университет «Высшая школа экономики», vol. 7(2), pages 139-172.
    4. Hyounggun Song & Sung Kwon Han & Seung Hwan Jeong & Hee Soo Lee & Kyong Joo Oh, 2019. "Using Genetic Algorithms to Develop a Dynamic Guaranteed Option Hedge System," Sustainability, MDPI, vol. 11(15), pages 1-12, July.
    5. Chen, An, 2005. "Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies," Bonn Econ Discussion Papers 19/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).

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