Efficient And Precise Computation Of Convolutions: Applying Fft To Heavy Tailed Distributions

2008 Computational Methods in Applied Mathematics  
In this paper we estimate and analyze the errors associated with the use of the discrete (fast) Fourier transformation for the numerical calculation of convolutions. We suggest and compare methods to reduce these errors without loosing the computational efficiency of the calculation scheme. A typical field of application of our findings is the calculation of aggregate loss distributions for, e.g., losses from insurance cases or operational risk losses in the finance industry. 2000 Mathematics
more » ... 2000 Mathematics Subject Classification: 42A38, 44A35, 60E10, 65R10, 90-08.
doi:10.2478/cmam-2008-0013 fatcat:6grq2er7evahzliwd57aocry6m