Hedging equity-linked life insurance contracts. (English) Zbl 1083.91546

Summary: This paper examines a portfolio of equity-linked life insurance contracts and determines risk-minimizing hedging strategies within a discrete-time setup. As a principal example, I consider the Cox-Ross-Rubinstein model and an equity-linked pure endowment contract under which the policyholder receives max(ST, K) at time T if he or she is then alive, where ST is the value of a stock index at the term T of the contract and K is a guarantee stipulated by the contract. In contrast to most of the existing literature, I view the contracts as contingent claims in an incomplete model and discuss the problem of choosing an optimality criterion for hedging strategies. The subsequent analysis leads to a comparison of the risk (measured by the variance of the insurer’s loss) inherent in equity-linked contracts in the two situations where the insurer applies the risk-minimizing strategy and the insurer does not hedge. The paper includes numerical results that can be used to quantify the effect of hedging and describe how this effect varies with the size of the insurance portfolio and assumptions concerning the mortality.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B28 Finance etc. (MSC2000)
Full Text: DOI


[1] Aase K. K., Scandinavian Actuarial Journal pp 26– (1994) · Zbl 0814.62067
[2] Baxter M., Financial Calculus: An Introduction to Derivative Pricing (1996) · Zbl 0858.62094
[3] Brennan M. J., Journal of Financial Economics 3 pp 195– (1976)
[4] Brennan M. J., Journal of Business 52 pp 63– (1979)
[5] Brennan M. J., Pricing Aad Investment Strategies for Guaranteed Equity-Linked Life Insurance (1979)
[6] Cox J., Journal of Financial Economics 7 pp 229– (1979) · Zbl 1131.91333
[7] Cvitanić J., SIAM Journal on Control and Optimization 38 pp 1050– (2000) · Zbl 1034.91037
[8] Delbaen F., Bulletin de l’Association Royale des Actuaires Belges pp 33– (1986)
[9] El Karoui N., SIAM Journal on Control and Optimization 33 pp 29– (1995) · Zbl 0831.90010
[10] Föllmer H., Finance and Stochastics 3 pp 251– (1999) · Zbl 0977.91019
[11] Föllmer H., Finance and Stochastics 4 pp 117– (2000) · Zbl 0956.60074
[12] Föllmer H., ASTIN Bulletin 18 pp 147– (1988)
[13] Föllmer H., Contributions to Mathematical Economics pp 205– (1986)
[14] Møller T., ASTIN Bulletin 28 pp 17– (1998) · Zbl 1168.91417
[15] Møller T., Finance and Stochastics (2001)
[16] Nielsen J., Insurance: Mathematics and Economics 16 pp 225– (1995) · Zbl 0872.62094
[17] Pliska S. R., Introduction to Mathematical Finance: Discrete Time Models (1997)
[18] Schweizer M., Hedging of Options in a General Semimartingale Model (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.