= Hedging a Gaussian income stream with exponential utility
{title2=$\pi^*=\mu/(\gamma\sigma^2)-\rho b/\sigma$}
An income stream with per-period <variance> $b^2$ and <correlation> $\rho$ with a <Gaussian> traded price increment produces a hedge holding $-\rho b/\sigma$ in addition to speculative demand. The residual income <variance> is $b^2(1-\rho^2)$. With independent period pairs, the same conditional quadratic minimization applies at each date. A deterministic income fee changes the optimized value but not the hedge holding.
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