= Solution
{c}
For simple predictable integrands, the <Itô integral> is a continuous square-integrable martingale and the <Itô isometry> gives
$$
\left\|\int_0^t(H_s-K_s)\,dW_s\right\|_2^2=\mathbb E\int_0^t|H_s-K_s|^2ds.
$$
Approximate a general square-integrable predictable integrand by simple ones. The resulting integral martingales are Cauchy in terminal $L^2$ norm. <Completeness of continuous square-integrable martingales> guarantees a unique continuous martingale limit, independent of the approximation, which defines the integral on the completed integrand space.
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