Let $S_{t}=S_{0}+\sigma B_{t}$
(a) Find the predictable representation for $Y=g\left(S_{T}\right)$, where $g$ is a given function. It is assumed that $E|Y|<\infty$
(b) Specify this for $g(x)=(x-K)^{+}$
My attempt
I am not sure if I have the right idea but this is what I have so far:
Theorem
$B_t$ has predictable representation property. Moreover Y is $F_t$ measurable and we know it is $E |Y|<\infty$. Therefore:
$Y=E Y+\int_{0}^{T} H_{S} d B_{s}$
Not sure how do I proceed forward.