what are the main drawbacks of using monté carlo methods ?
I've never seen the accent on the "e" like that before. I thought it was from Italian and doesn't have an accent? Not too sure.
Anyway I would say the main disadvantage is that it could take a prohibitively long time to get an answer to required precision; for example, getting 5 decimal places (with, say, 99% confidence) might a quadrillion trials depending on what you're dealing with.
Monte-Carlo indeed is Italian. And there's indeed no accent.
French deformation
Yeah, the main problem is the precision. To get a 10 times better precision, you have to make 100 times more simulations, and that can be quite a lot... (because the central limit theorem gives a convergence speed in $\displaystyle \frac{1}{\sqrt{n}}$)