Pricing in General Insurance

249Aggregate Loss Modelling

17.3.1.2.2 Aliasing Problem

A problem related to that of choosing the correct parameters for the numerical evaluation

of the aggregate loss distribution is that of aliasing. This happens when the probability of

the severity being above M × h, 1 − F

X

(M × h), is signicant. This residual probability ends

up being wrapped around and distributed over the range (0,…M − 1).

To get around this problem, a so-called tilting procedure has been suggested by Grübel

and Hermesmeir (see Embrechts and Frei [2009] for full references). This works by xing

a value θ and replacing the original vector f with T

θ

f = ( f

0

, e

−θ

f

1

, e

−2θ

f

2

,…e

−(M−1)θ

f

M−1

), where

T

θ

is the tilting operator. If the choice of θ is adequate, this causes t ...