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Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies

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  • Chen, An
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Abstract

The present paper investigates the net loss of a life insurance company issuing equity-linked pure endowments in the case of periodic premiums. Due to the untradability of the insurance risk which affects both the in- and outflow side of the company, the issued insurance claims cannot be hedged perfectly. Furthermore, we consider an additional source of incompleteness caused by trading restrictions, because in reality the hedging of the contingent claims is more likely to occur at discrete times. Based on Møller [Møller, T., 1998. Risk-minimizing hedging strategies for unit-linked life insurance contracts. Astin Bull. 28, 17-47], we particularly examine the situation, where the company applies a time-discretized risk-minimizing hedging strategy. Through an illustrative example, we observe numerically that only a relatively small reduction in ruin probabilities is achieved with the use of the discretized originally risk-minimizing strategy because of the accumulated extra duplication errors caused by discretizing. However, the simulated results are highly improved if the hedging model instead of the hedging strategy is discretized. For this purpose, Møller's [Møller, T., 2001. Hedging equity-linked life insurance contracts. North Amer. Actuarial J. 5 (2), 79-95] discrete-time (binomial) risk-minimizing strategy is adopted.

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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 42 (2008)
Issue (Month): 3 (June)
Pages: 1035-1049

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Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1035-1049

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Web page: http://www.elsevier.com/locate/inca/505554

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  1. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 36(3), pages 499-516, June.
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  4. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 12(3), pages 245-257, June.
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  6. An Chen & Michael Suchanecki, 2006. "Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities," Bonn Econ Discussion Papers, University of Bonn, Germany bgse8_2006, University of Bonn, Germany.
  7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  8. Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B, University of Bonn, Germany 291, University of Bonn, Germany, revised Mar 1995.
  9. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 13(3), pages 303-304, December.
  10. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers, University of Aarhus, Aarhus School of Business, Department of Business Studies 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
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