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Fundamental theorem of asset pricing: a strengthened version and а martingale measures search area

https://doi.org/10.29235/1561-8323-2022-66-2-135-140

Abstract

In the article a strengthened version of the ’Fundamental Theorem of Asset Pricing’ for a one-period market model is proven. The principal role in this result is played by total and nonanihilating cones.

About the Authors

A. V. Lebedev
Belarusian State University
Belarus

Lebedev Andrei V. – D. Sc. (Physics and Mathematics), Professor, Head of the Department

4, Nezavisimosti Ave., 220050, Minsk



G. S. Romashchenko
Belarusian State University
Belarus

Romashchenko Galina S. – Ph. D. (Physics and Mathematics), Associate Professor

4, Nezavisimosti Ave., 220050, Minsk



P. P. Zabreiko
Belarusian State University
Belarus

Minsk



References

1. Delbaen F., Schachermayer W. The Mathematics of Arbitrage. Springer Finance, 2006. https://doi.org/10.1007/978-3-540-31299-4

2. Schachermayer W. Fundamental theorem of asset pricing. Encyclopedia of Quantitative Finance, 2010, no. 2, pp. 792–801. https://doi.org/10.1002/9780470061602.eqf04002

3. Zabreiko P. P., Lebedev A. V. Banach geometry of financial market models. Doklady Mathematics, 2017, vol. 95, no. 2, pp. 164–167. https://doi.org/10.1134/s106456241702020x

4. Lebedev A. V., Zabreiko P. P. Banach geometry of arbitrage free markets. Positivity, 2021, vol. 25, no. 2, pp. 679–699. https://doi.org/10.1007/s11117-020-00782-6

5. Follmer H., Schied A. Stochstic Finance: An Introduction in Discrete Time. 2nd rev. and extended ed. Berlin, New York, Walter de Guyter, 2004. https://doi.org/10.1515/9783110212075


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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)