Symmetric Integrals and Their Application in Financial Mathematics

F. S. Nasyrov

Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 265-278.

Résumé

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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