= Forward drift restriction for square-root stock claims
{title2=$A_t(T)=B_t(T)(\int_t^TB_t(u)du-\sigma_t/2)$}
If $\mathbb E[\sqrt{S_T}\mid\mathcal F_t]=\sqrt{S_t}\exp(-\int_t^Tf_t(u)du)$ and $df_t(T)=A_t(T)dt+B_t(T)dW_t$, the <stochastic Fubini theorem> and <Itô formula> give $f_t(t)=\sigma_t^2/8$ and $A_t(T)=B_t(T)(\int_t^TB_t(u)du-\sigma_t/2)$. The final term comes from the product cross-variation. Continuity extends the drift equality to the specified continuous versions.
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