Hostname: page-component-5b777bbd6c-f9nfp Total loading time: 0 Render date: 2025-06-21T12:26:07.929Z Has data issue: false hasContentIssue false
  • English
  • Français

Risk-Minimizing Hedging Strategies for Unit-Linked Life Insurance Contracts

Published online by Cambridge University Press:  29 August 2014

Thomas Møller
Thomas Møller*
Affiliation:
Laboratory of Actuarial Mathematics, University of Copenhagen
*
Laboratory of Actuarial Mathematics, Universitetsparken5, DK-2100 Copenhagen Ø, DenmarkE-mail:tmoller@math.ku.dk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A unit-linked life insurance contract is a contract where the insurance benefits depend on the price of some specific traded stocks. We consider a model describing the uncertainty of the financial market and a portfolio of insured individuals simultaneously. Due to incompleteness the insurance claims cannot be hedged completely by trading stocks and bonds only, leaving some risk to the insurer. The theory of risk-minimization is briefly reviewed and applied after a change of measure. Risk-minimizing trading strategies and the associated intrinsic risk processes are determined for different types of unit-linked contracts. By extending the model to the situation where certain reinsurance contracts on the insured lives are traded, the direct insurer can eliminate the risk completely. The corresponding self-financing strategies are determined.

Keywords

Incomplete marketMartingale representationMinimal martingale measureIntrinsic riskReinsurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 17 - 47
Copyright
Copyright © International Actuarial Association 1998

References

REFERENCES

Aase, K.K. and Persson, S.A. (1994). Pricing of Unit-linked Life insurance Policies, Scandinavian Actuarial Journal 1, 26–52.CrossRefGoogle Scholar
Bacinello, A.R. and Ortu, F. (1993). Pricing equity-linked life insurance with endogenous minimum guarantees, Insurance: Mathematics and Economics 12, 245–257.Google Scholar
Björk, T. (1996). Arbitrage Theory in Continuous Time, Stockholm School of Economics.Google Scholar
Brennan, M.J. and Schwartz, E.S. (1979). Pricing and investment strategies for equity-linked life insurance, Monograph no. 7/The S.S. Huebner Foundation for insurance education, Wharton School, University of Pennsylvania, Philadelphia.Google Scholar
Delbaen, F. (1990). Equity linked Policies, Bulletin Association Royal Actuaires Beiges, 33–52.Google Scholar
Duffie, D. (1996). Dynamic Asset Pricing Theory, 2nd ed., Princeton University Press, Princeton, New Jersey.Google Scholar
Ekern, S.E. and Persson, S.-A. (1996). Exotic Unit-Linked Life Insurance Contracts, The Geneva Papers on Risk and Insurance Theory 21(1), 35–63.CrossRefGoogle Scholar
Follmer, H. and Sondermann, D. (1986). Hedging of non-redundant Contingent Claims, in: Contributions to Mathematical Economics, eds. Hildenbrand, W. and Mas-Colell, A., 205–223.Google Scholar
Föllmer, H. and Schweizer, M. (1988). Hedging by sequential regression: An introduction to the mathematics of option trading, The ASTIN Bulletin 18(2), 147–160.CrossRefGoogle Scholar
Ikeda, N. and Watanabe, S. (1981). Stochastic Differential Equations and Diffusion Processes, North-Holland.Google Scholar
Lamberton, D. and Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall.Google Scholar
Møller, T. (1996). Risk-minimizing strategies for unit-linked life insurance products, Master's thesis, University of Copenhagen.Google Scholar
Møller, T. (1998). Risk-minimizing hedging strategies for general payment processes, Working paper, Laboratory of Actuarial Mathematics, University of Copenhagen. (Forthcoming).Google Scholar
Nielsen, J. and Sandmann, K. (1995). Equity-linked Life Insurance: A Model with Stochastic Interest Rates, Insurance: Mathematics and Economics 16, 225–253.Google Scholar
Norberg, R. (1992). Hattendorff's Theorm and Thiele's Differential Equation Generalized, Scandinavian Actuarial Journal 1, 2–14.CrossRefGoogle Scholar
Norberg, R. (1995). Differential equations for moments of present values in life insurance, Insurance: Mathematics and Economics 17, 171–180.Google Scholar
Norberg, R. and MøLler, C.M. (1996). Thiele's Differential Equation with Stochastic Interest of Diffusion Type, Scandinavian Actuarial Journal 1, 37–49.CrossRefGoogle Scholar
Schwartz, H.R. (1989). Numerical Analysis. A Comprehensive Introduction, John Wiley & Sons Ltd.Google Scholar
Schweizer, M. (1991). Option hedging for semimartingales, Stochastic Processes and their Applications 37, 339–363.CrossRefGoogle Scholar
Schweizer, M. (1994). Risk-minimizing hedging strategies under restricted information, Mathematical Finance 4, 327–342.CrossRefGoogle Scholar
Schweizer, M. (1995). On the Minimal Martingale Measure and the Follmer-Schweizer Decomposition, Stochastic Analysis and Applications 13, 573–599.CrossRefGoogle Scholar