FFT2: Fast Fourier Transform

In lucazama/CollectiveRisk: Collective Risk Model Functions.

Description

Computes the Fast Fourier Approximation to P(S>m), where S is the aggregate claim size.

Usage

FFT2 (fx,fm, n,lower,upper, m )

Arguments

fx	CDF of the claim intesities.
n	number of points used in the discretization (possibly a power of 2)
lower	starting point of the discretization of X
upper	end point of the discretization of X
m	approximation to P(S>m)
fm	Moment generating function of the Claim frequency.

Details

The function works for any aggregate claim distribution. It is not that stable when the lower and upper bounds are not selected with accuracy. (be sure to consider a great part of the domain of X)

Value

the function returns P(S>m)

Note

the discretization bounds (lower and upper) are generally different from those of FFT. In FFT the discretization regards S, in FFT2 it concerns X.

References

"Panjer Recursion versus FFT For Compound Distributions", Paul Embrechets and Marco Frei (2009), Mathematical Methods of Operations Research.

See Also

FFT

Examples

FFT2(fx=function(x) pgamma(x,40,2),fM= function(t) exp(30*(exp(t)-1)),n=2^19, lower=0, upper=3000,m=900)

lucazama/CollectiveRisk documentation built on July 25, 2020, 7:22 a.m.