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vonjd
vonjd
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Here is my two cents on an intuitive explanation of the Ito integral:

The Ito integral is \int_S^T f(t,w) dB(t,w)$\int_S^T f(t,w) dB(t,w)$

We can thing of B(t,w)$B(t,w)$, the Brownian motion as the actual price (with mean subtracted) and f(t,w)$f(t,w)$ is a random trading action and its gain on the observable prices. As a result, f(t,w) $f(t,w)$ is F_t$F_t$ adaptive, i.e., it can be dependent only on the history of the prices not future prices. Then, the Ito integration is the total gain from S$S$ to T$T$ using random trading action+gain f(t,w)$f(t,w)$.

Here is my two cents on an intuitive explanation of the Ito integral:

The Ito integral is \int_S^T f(t,w) dB(t,w)

We can thing of B(t,w), the Brownian motion as the actual price (with mean subtracted) and f(t,w) is a random trading action and its gain on the observable prices. As a result, f(t,w) is F_t adaptive, i.e., it can be dependent only on the history of the prices not future prices. Then, the Ito integration is the total gain from S to T using random trading action+gain f(t,w).

Here is my two cents on an intuitive explanation of the Ito integral:

The Ito integral is $\int_S^T f(t,w) dB(t,w)$

We can thing of $B(t,w)$, the Brownian motion as the actual price (with mean subtracted) and $f(t,w)$ is a random trading action and its gain on the observable prices. As a result, $f(t,w)$ is $F_t$ adaptive, i.e., it can be dependent only on the history of the prices not future prices. Then, the Ito integration is the total gain from $S$ to $T$ using random trading action+gain $f(t,w)$.

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beginner
beginner
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Here is my two cents on an intuitive explanation of the Ito integral:

The Ito integral is \int_S^T f(t,w) dB(t,w)

We can thing of B(t,w), the Brownian motion as the actual price (with mean subtracted) and f(t,w) is a random trading action and its gain on the observable prices. As a result, f(t,w) is F_t adaptive, i.e., it can be dependent only on the history of the prices not future prices. Then, the Ito integration is the total gain from S to T using random trading action+gain f(t,w).