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Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies

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  • An Chen
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Abstract

In this paper, we consider the net loss of a life insurance company issuing identical equity-linked pure endowment contracts in the case of periodic premiums. Under this construction, financial risks as well as the mortality risk are included. Based on Møller (1998), we particularly investigate the situation where the company applies a time-discretized risk-minimizing hedging strategy, i.e., a trading restriction is imposed on a continuous-time risk-minimizing strategy. Therefore, the considered model is incomplete where the incompleteness results not only from the mortality risk but also from the trading restrictions. Through an illustrative example, it is observed from the simulations that a substantial reduction in the ruin probability is achieved by using the time-discretized risk-minimizing strategy. However, as the hedging frequency is set higher, this advantage almost disappears, because a higher frequency leads to more hedging errors which constitute a vital part of the hedger’s net loss. In order to improve the simulated results, another type of discrete-time risk-minimizing strategy is taken into consideration. It is obtained by discretizing the hedging model instead of the hedging strategy. For this purpose, Møller’s (2001) discrete-time (binomial) risk-minimizing strategy is adopted. For both strategies, a number of sensitivity analyses are carried out, e.g. how the ruin probability changes with the fair combination of the minimum interest rate guarantee and the participation rate.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse19_2005.

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Length: 28
Date of creation: Aug 2005
Date of revision:
Handle: RePEc:bon:bonedp:bgse19_2005

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Keywords: Net Loss; Discrete-time Risk-minimizing Hedging Strategies; Pure Endowment Equity-linked Life Insurance;

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  1. An Chen & Michael Suchanecki, 2006. "Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities," Bonn Econ Discussion Papers bgse8_2006, University of Bonn, Germany.
  2. Antje Mahayni & Erik Schlögl, 2003. "The Risk Management of Minimum Return Guarantees," Research Paper Series 102, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
  4. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
  5. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 35-63, June.
  6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  7. J. Aase Nielsen & Klaus Sandmann, 1996. "Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 65-102, June.
  8. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
  9. 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, vol. 36(3), pages 499-516, June.
  10. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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