All the recent copula based models for CDOs and basket tend to massively use numerical integration schemes...what is the best scheme to adopt and can you suggest any tutorial or webiste or library presenting methods fo numerical integration with infinite limits?Thanks,S

Some ideas, as always, depending on your goals:1. Put the integral into Mathematica2. Transform the infinite region into a finite region, like [1, infty) -> (0, 1] by 1/x3. Try Monte Carlo integration

but numerical integration for copulas is really much easier than the general infinite integration problem... the probability CDF automatically gives you a map from [0,1] onto the output space, and practically speaking the output space is also compact because the tails die off so quickly. The hard part is when you need the infinite integral of an arbitrary function where you don't know the function's 'material support', or where the dimensionality is high and similar problem appears but across dimensions. In either case you are ultimately looking for some version of sampling stratification which will make the integral more Lebesgue-like and less Riemann-like. You will chop up the sample space so that either the function takes lots of values, or its derivatives take lots of values or whatever. Sampling many times where the function doesn't really change is clearly a waste of time.