Suppose that $X$ and $Y$ are independent log normal random variables. Is it possible to compute a closed form solution (or approximate closed form) to the expected value of $X/(X+Y)$?
I know that the sum of log normal random variables does not have a simple distribution as discussed here. How about the expected value of $X_1/(X_1+...X_n)$ where $X_i$ are independent log normal random variables?