I want to calculate numerically the expectation of a lognormal random variable $Y=e^X$, where $X$ is normally distributed with mean $m$ and variance $V$.
The expectation is known as $e^{m+\frac{1}{2}V}$. When it comes to simulation , we can generate $N$ random numbers $\{Y_{k}\}_{k=1}^{N}$ centered normally distributed, and calculate : $\frac{1}{N}\sum_{k=1}^{N}{e^{m+\sqrt{V}Y_k}}$.
When $m$ and $V$ are relatively small, we can replicate the expected value. When $m$ and $V$ are very high, we get ridiculously high number.
What is the best method to reduce that kind of numerical errors?
Thanks.