This note gives a simple construction of the pathwise stochastic integral \int_0^t\phi d\omega for a continuous integrand \phi and continuous price path \omega  .
This note gives a simple construction of the pathwise stochastic integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator. A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's .
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and
whose variation index is finite and a
A
as integrator. A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's