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Risk-minimizing hedging strategies for unit-linked life insurance contracts. (English) Zbl 1168.91417

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G10 Portfolio theory
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[1] DOI: 10.1080/07362999508809418 · Zbl 0837.60042
[2] Stochastic Differential Equations and Diffusion Processes (1981)
[3] DOI: 10.2143/AST.18.2.2014948
[4] Contributions to Mathematical Economics pp 205– (1986)
[5] DOI: 10.1007/BF00949050
[6] Dynamic Asset Pricing Theory (1996)
[7] Bulletin Association Royal Actuaires Beiges pp 33– (1990)
[8] Pricing and investment strategies for equity-linked life insurance (1979)
[9] Arbitrage Theory in Continuous Time (1996)
[10] Insurance: Mathematics and Economics 12 pp 245– (1993)
[11] Scandinavian Actuarial Journal 1 pp 26– (1994)
[12] DOI: 10.1016/0304-4149(91)90053-F · Zbl 0735.90028
[13] Numerical Analysis. A Comprehensive Introduction (1989)
[14] Scandinavian Actuarial Journal 1 pp 37– (1996)
[15] Insurance: Mathematics and Economics 17 pp 171– (1995)
[16] Scandinavian Actuarial Journal 1 pp 2– (1992)
[17] Insurance: Mathematics and Economics 16 pp 225– (1995)
[18] Risk-minimizing hedging strategies for general payment processes (1998)
[19] Introduction to Stochastic Calculus Applied to Finance (1996)
[20] DOI: 10.1111/j.1467-9965.1994.tb00062.x · Zbl 0884.90051
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