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Tr. Mat. Inst. Steklova, 2002, Volume 237, Pages 265–278 (Mi tm338)  

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 237, 256–269

Bibliographic databases:
UDC: 519.2+519.8
Received in July 2000

Citation: F. S. Nasyrov, “Symmetric Integrals and Their Application in Financial Mathematics”, Stochastic financial mathematics, Collected papers, Tr. Mat. Inst. Steklova, 237, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 265–278; Proc. Steklov Inst. Math., 237 (2002), 256–269

Citation in format AMSBIB
\Bibitem{Nas02}
\by F.~S.~Nasyrov
\paper Symmetric Integrals and Their Application in Financial Mathematics
\inbook Stochastic financial mathematics
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2002
\vol 237
\pages 265--278
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm338}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1976522}
\zmath{https://zbmath.org/?q=an:1034.60056}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 237
\pages 256--269


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. S. Nasyrov, “Symmetric integrals and stochastic analysis”, Theory Probab. Appl., 51:3 (2007), 486–503  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. O. V. Zakharova, “Solution of one class of systems of stochastic differential equations”, Russian Math. (Iz. VUZ), 53:6 (2009), 1–6  mathnet  crossref  mathscinet  zmath
    3. F. S. Nasyrov, “Ob obobschennoi formule Tanaki”, Ufimsk. matem. zhurn., 1:1 (2009), 69–76  mathnet  zmath
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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