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  .
This note gives a simple construction of the pathwise It\^o 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 . Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
R
stochastic
It\^o
A
. Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value