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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 237, Pages 265–278
(Mi tm338)
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This article is cited in 3 scientific papers (total in 3 papers)
Symmetric Integrals and Their Application in Financial Mathematics
F. S. Nasyrov Ufa State Aviation Technical University
Abstract:
Symmetric Stieltjes integrals $\int _0^t f(s)*dX(s)$ are constructed for arbitrary continuous functions $X(s)$ of unbounded variation. Within the framework of this construction, the pathwise symmetric integrals $\int _0^t f(s)dX(s)$ coincide with the Stratonovich stochastic integrals for a random Brownian motion $X(s)=X(s,\omega )$. It is shown that a symmetric integral can be extended as an integral with respect to a certain type of charge. By the technique of symmetric integrals, the price of European call options is determined in the pathwise model of a $(B,S)$ market.
Received in July 2000
Citation:
F. S. Nasyrov, “Symmetric Integrals and Their Application in Financial Mathematics”, Stochastic financial mathematics, Collected papers, Trudy Mat. Inst. Steklova, 237, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 265–278; Proc. Steklov Inst. Math., 237 (2002), 256–269
Linking options:
https://www.mathnet.ru/eng/tm338 https://www.mathnet.ru/eng/tm/v237/p265
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Abstract page: | 626 | Full-text PDF : | 403 | References: | 57 |
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