 Hedging a Gaussian income stream with exponential utility

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.