= Power transformation of a complete-market investment equation
{title2=$f=g^R$}
For a complete-market <investment-consumption problem> with <constant relative risk aversion utility>, the nonlinear wealth-homogeneity coefficient equation may contain $f^{\prime2}/f$. Writing $f=g^R$ cancels this gradient square against the one from $f^{\prime\prime}$. In the index-driven correlation model the result is $\sigma_0^2g^{\prime\prime}/2+Bg^\prime-\delta(m)g+1=0$, a <linear differential equation>; the positive economic solution gives consumption $w/g$.
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