On the pricing of equity-linked life insurance contracts in Gaussian financial environment
Authors:
A. V. Melnikov and M. L. Nechaev
Journal:
Theor. Probability and Math. Statist. 70 (2005), 105-111
MSC (2000):
Primary 60H30; Secondary 91B28, 91B30
DOI:
https://doi.org/10.1090/S0094-9000-05-00634-4
Published electronically:
August 12, 2005
MathSciNet review:
2109827
Full-text PDF Free Access
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Abstract: The paper deals with the problem of pricing an equity-linked insurance contract based on stock prices. The stock prices are supposed to follow a stochastic exponent model with respect to a given Gaussian martingale. The model gives a possibility to obtain unified formulas for “mean–variance” hedging and the corresponding premium for both natural cases: Black–Scholes and Gaussian discrete time models.
References
- O. Glonti and Z. Khechinashvili, Financial $(B,S)$-market with Gaussian martingale. Mean square optimal hedging strategies, Proc. A. Razmadze Math. Inst. 115 (1997), 33–43 (English, with English and Georgian summaries). MR 1639100
- R. Sh. Liptser and A. N. Shiryaev, Teoriya martingalov, Teoriya Veroyatnosteĭ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], “Nauka”, Moscow, 1986 (Russian). MR 886678
- T. Møller, Risk-minimizing hedging strategies for unit-linked life insurance contracts, Astin Bulletin 28 (1998), no. 1.
- Albert N. Shiryaev, Essentials of stochastic finance, Advanced Series on Statistical Science & Applied Probability, vol. 3, World Scientific Publishing Co., Inc., River Edge, NJ, 1999. Facts, models, theory; Translated from the Russian manuscript by N. Kruzhilin. MR 1695318
References
- O. Glonti and Z. Khechinashvili, Financial $(B,S)$-market with Gaussian martingale mean square optimal hedging strategies, Proc. A. Razmadze Math. Inst. 115 (1997), 33–43. MR 1639100 (99j:90010)
- R. Liptser and A. N. Shiryaev, Theory of Martingales, “Nauka”, 1986. (Russian) MR 0886678 (88h:60091)
- T. Møller, Risk-minimizing hedging strategies for unit-linked life insurance contracts, Astin Bulletin 28 (1998), no. 1.
- A. N. Shiryaev, Essentials of Stochastic Financial Mathematics, World Sci., River Edge, NJ, 1999. MR 1695318 (2000e:91085)
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Additional Information
A. V. Melnikov
Affiliation:
Steklov Mathematical Institute, Gubkina 8, Moscow 117966, Russia
Address at time of publication:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
M. L. Nechaev
Affiliation:
Steklov Mathematical Institute, Gubkina 8, Moscow 117966, Russia
Keywords:
Hedging,
$(B, S)$-market,
contingent claim,
insurance liabilities,
insurance premiums and claims
Received by editor(s):
March 12, 2003
Published electronically:
August 12, 2005
Additional Notes:
This paper was partially supported by grants of NSERC and SSHRC
Article copyright:
© Copyright 2005
American Mathematical Society
