Periodic utility indifference payment for Gaussian income ($\overline{y}=a-\mu \rho b/\sigma -\gamma b^2(1-{\rho }^2)/2$)

For Gaussian income of mean $a$, standard deviation $b$ and tradable correlation $\rho$, exponential utility makes the maximum acceptable per-period fee equal to the mean minus the correlated-income hedge cost and the residual variance penalty. Compare optimized utilities with and without the contract; a fee above this level makes the contract strictly inferior. At perfect correlation the residual penalty vanishes, leaving only the mean and hedge-cost terms.