So I have an equation
$\displaystyle (\mu_i(t)-r_t)dt=\sum^K_{k=1}\beta_{ik}(t)(\mu_{X_k}(t)-r_t)dt$
where
$\displaystyle \beta_{ik}(t)=\frac{\frac{d<S_i,X_k>_t}{S_i(t)X_k( t)}}{\frac{d<X_k,X_k>_t}{X_k(t)^2}}$
So I have an equation
$\displaystyle (\mu_i(t)-r_t)dt=\sum^K_{k=1}\beta_{ik}(t)(\mu_{X_k}(t)-r_t)dt$
where
$\displaystyle \beta_{ik}(t)=\frac{\frac{d<S_i,X_k>_t}{S_i(t)X_k( t)}}{\frac{d<X_k,X_k>_t}{X_k(t)^2}}$