Hi all,I have to work with a numerical integration of a complex-valued function in my pricing model. The integral is meant to be the inverse Fourier integral. The integrand is complicated and complex valued. It has lots of singularities and branch points. I am not sure how to do the integral treating these branch points and singularities. Are there good resources that can handle these situations? Please kindly give me some pointers!Thanks a lot!

As far as online resources go I find Chen's lecture notes pretty useful in this respect.As for papers dealing with Fourier inversion, given your previous post I'm sure you've already found one paper that could be useful.

You might also find of interest:Carr Peter, Hélyette Geman, Dilip Madan, Liuren Wu, Marc Yor 'Option Pricing using Integral Transforms' 2/03 <FFT, jumps, Poisson, convexity, time changed, activity rate, Fourier, characteristics function, inversion, Lévy–Khintchine, jump, convexity, time change> [on P. Carr's Web site www.petercarr.net under Presentations]Davies R. 'Numerical Inversion of a Characteristic Function' Biometrika 73Pinsky Mark, Michael Taylor 'Pointwise Fourier Inversion: A Wave Equation Approach' Sepp Artur 'Fourier Inversion Methods for Option Pricing under Jump-Diffusion Stochastic Volatility & Lévy Processes' 9/02 <Variance-Gamma, V-G>Abate Joseph, Gagan Choudhury, Ward Whitt 'An Introduction to Numerical Transform Inversion & Its Application to Probability Models' 99 Bakshi Gurdip, Dilip Madan 'Spanning & Derivative Security Valuation' Journal of Financial Economics 2000 <Arrow-Debreu, Characteristic function, average rate, correlation options> Abate Joseph, Ward Whitt 'Numerical Inversion of Laplace Transforms of Probability Distributions' J. Computing 95 Abate Joseph, Ward Whitt 'The Fourier-Series Method for Inverting Transforms of Probability Distributions' Queuing Systems 92 v.10 5-88 <Laplace, tail probability, Gaver-Stehfest>Scott L. 'Pricing Stock Options in a Jump-Diffusion Model with Stochastic Volatility & Interest Rates:Applications of Fourier Inversion Methods' Mathematical Finance 11/97