= Merton consumption-investment problem
{c}
{title2=$c^*=\delta w,\quad \theta^*=(\mu-r)w/(R\sigma^2)$}
For a constant-coefficient single-asset <investment-consumption problem> with <constant relative risk aversion utility>, put $\kappa=(\mu-r)/\sigma$ and $\delta=[\rho-(1-R)(r+\kappa^2/(2R))]/R$. When $\delta>0$, the infinite-horizon value is $\delta^{-R}w^{1-R}/(1-R)$ and the optimal controls are $c^*=\delta w$ and $\theta^*=(\mu-r)w/(R\sigma^2)$. The case $R=1$ uses logarithmic utility.
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