Suppose we have $X,Y$ independent normally distributed r.v. $X \sim \mathcal N(a,\sigma^2_1)$, $Y \sim \mathcal N(a,\sigma^2_2)$, and $Z=\rho X+\sqrt{1-\rho^2}Y$ where $\rho$ is some constant.
How can I calculate the $\mathbb{E}[\max(0,e^Z-e^Y)]$?
Thanks.