State-dependent correlation investment problem
= State-dependent correlation investment problem
{title2=$\rho=\rho(M)$}
When asset correlation varies with a traded market index, the index is both an asset and a state variable. Writing $m=\log M$ and optimizing <Brownian portfolio exposures> accounts for the cross derivative between wealth and $m$. Power <homogeneity> reduces the <Hamilton-Jacobi-Bellman equation> to an ordinary differential equation in $m$.