Etude des marchés d'assurance non-vie à l'aide d'équilibres de ...

tel-00703797, version 2 - 7 Jun 2012
Chapitre 1. Sur la nécessité d’un modèle de marché
distance
0 20 40 60 80 100 120
Gaussian Kernel smoothing
bandwidth=1
bandwidth=2
bandwidth=3
5 10 15 20 25
speed
(a) Kernel smoothing
distance
0 20 40 60 80 100 120
degree=1
degree=2
degree=4
B-splines smoothing
5 10 15 20 25
speed
(b) B-spline smoothing
Figure 1.6: Kernel and B-spline smoothing
A crucial fact is that using K polynomials can be represented by a banded matrix, a band
for each segment. Using the matrix representation emphasizes that we use a basis of functions
to approximate the function f. Many polynomial basis can be used (e.g. Bernstein polynoms
for Bézier curves).
One popular basis is the B-spline basis. They are defined recursively starting polynoms of
degree 0 defined by Bi,0(t) = 1ti≤t