Geodesic
Symmetric Integrals and Their Application in Financial Mathematics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 265-278

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {F. S. Nasyrov},
     title = {Symmetric {Integrals} and {Their} {Application} in {Financial} {Mathematics}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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F. S. Nasyrov. Symmetric Integrals and Their Application in Financial Mathematics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 265-278. http://geodesic.mathdoc.fr/item/TM_2002_237_a16/