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Tr. Mat. Inst. Steklova, 2002, Volume 237, Pages 57–79 (Mi tm324)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Unity of Quantitative Methods of Pricing in Finance and Insurance

A. V. Melnikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A relationship between the calculation of premiums and reserves in insurance and finance is studied. It is shown how traditional actuarial methods of calculation in property insurance are derived from the financial no-arbitrage principle. A general method is presented for estimating the probability of ruin of an insurance company. In life insurance, the main emphasis is placed on the description of innovation schemes of “flexible” insurance, and it is pointed out that the calculation of the corresponding premiums and reserves is related with the Black–Scholes formula and equation. A new approach to the insurance and reinsurance of catastrophic risks is presented which is based on their diversification on financial markets by means of insurance derivative securities.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 237, 50–72

Bibliographic databases:

UDC: 519.816
Received in August 2001

Citation: A. V. Melnikov, “On the Unity of Quantitative Methods of Pricing in Finance and Insurance”, Stochastic financial mathematics, Collected papers, Tr. Mat. Inst. Steklova, 237, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 57–79; Proc. Steklov Inst. Math., 237 (2002), 50–72

Citation in format AMSBIB
\Bibitem{Mel02}
\by A.~V.~Melnikov
\paper On the Unity of Quantitative Methods of Pricing in Finance and Insurance
\inbook Stochastic financial mathematics
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2002
\vol 237
\pages 57--79
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm324}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1976508}
\zmath{https://zbmath.org/?q=an:1033.91016}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 237
\pages 50--72


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Melnikov A.V., “Quantile hedging of equity-linked life insurance policies”, Dokl. Math., 69:3 (2004), 428–430  mathnet  mathscinet  zmath  isi
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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