Let (T>0). Show that for (f:[0, T] mapsto mathbb{R}) a differentiable function such that (f(T)=0), we have

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Let $T>0$. Show that for $f:[0, T] \mapsto \mathbb{R}$ a differentiable function such that $f(T)=0$, we have

\[\int_{0}^{T} f(t) d B_{t}=-\int_{0}^{T} f^{\prime}(t) B_{t} d t\]

Apply Itô's calculus to $t \mapsto f(t) B_{t}$.

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Introduction To Stochastic Finance With Market Examples

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Authors: Nicolas Privault

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Let (T>0). Show that for (f:[0, T] mapsto mathbb{R}) a differentiable function such that (f(T)=0), we have

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By the It formula 428 we have beginaligned dleftft Btight ft d BtBt d ftd ft cdot d Bt f...View the full answer

Introduction To Stochastic Finance With Market Examples

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