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

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

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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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
2. O. V. Zakharova, “Solution of one class of systems of stochastic differential equations”, Russian Math. (Iz. VUZ), 53:6 (2009), 1–6
3. F. S. Nasyrov, “Ob obobschennoi formule Tanaki”, Ufimsk. matem. zhurn., 1:1 (2009), 69–76
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