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Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts

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  • Pansera, Jérôme

Abstract

We develop a theory of local risk minimization for payment processes in discrete time, and apply this theory to the pricing and hedging of equity-linked life-insurance contracts. Thus, we extend the work of Møller (2001a) in several directions: from risk minimization (which is done under a martingale measure) to local risk minimization (which is done under an arbitrary measure), from single claims to payment processes, from complete financial markets to possibly incomplete financial markets, from a single risky asset to several risky assets, and from finite state spaces to general state spaces.

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  • Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:1-11
    DOI: 10.1016/j.insmatheco.2011.10.001
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    References listed on IDEAS

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    1. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    2. X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
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    13. 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.
    14. Serena Tiong, 2000. "Valuing Equity-Indexed Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 149-163.
    15. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.
    16. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
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    4. Raimund M. Kovacevic, 2019. "Valuation and pricing of electricity delivery contracts: the producer’s view," Annals of Operations Research, Springer, vol. 275(2), pages 421-460, April.

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