TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
HdR
1. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
Contributions to Dependence Modeling*
A. Charpentier (Université de Rennes 1)
Habilitation à Diriger des Recherches,
Rennes, 2016.
@freakonometrics 1
2. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
2006-2016, Brief Summary
2006: PhD in Applied Mathematics
Depedencies, with Applications in Insurance and Finance
Supervised by Jan Beirlant & Michel Denuit
2006-2010: Maître de Conférences
Université de Rennes 1
2010-2014: Professeur
Université du Québec à Montréal
2014-2016: Maître de Conférences
Université de Rennes 1
@freakonometrics 2
3. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Dependence & Extremes
with Anne-Laure Fougères, Christian Genest & Johanna Nešlehová Multivariate
Archimax Copulas (JMVA, 2014).
Let be a d-variate stable tail dependence function
and φ be the generator of a d-variate Archimedean
copula. Then
Cφ, (u1, · · · , ud) = φ−1
[ (φ(u1) + · · · + φ(ud))]
is a d-dimensional copula. Further, if 1 − ψ(1/s)
is regularly varying (at ∞) with index α ∈ [0, 1],
Cφ, ∈ MDA(C ),
C (u1, · · · , ud) = exp − α
| log(u1)|
1
α , · · · , | log(ud)|
1
α
see results obtained with Johan Segers Tails of Archimedean Copulas (JMVA).
@freakonometrics 3
4. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Nonparametric estimation (and Borders)
with Emmanuel Flachaire Transformed Kernel & Inequality and Risk Indices
(Actualité Économique, 2015)
Density
−2 −1 0 1 2
0.00.10.20.30.40.50.6
Density
−2 −1 0 1 2
0.00.10.20.30.40.50.6
Density
−2 −1 0 1 2
0.00.10.20.30.40.50.6
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
@freakonometrics 4
5. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Nonparametric estimation (and Borders)
with Emmanuel Flachaire Transformed Kernel & Inequality and Risk Indices
(Actualité Économique, 2015)
Density
0.0 0.2 0.4 0.6 0.8 1.0
0.00.51.01.52.0
Density
0.0 0.2 0.4 0.6 0.8 1.0
0.00.51.01.52.0
Density
0.0 0.2 0.4 0.6 0.8 1.0
0.00.51.01.52.0
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
Density
0 2 4 6 8 10 12
0.00.10.20.30.40.50.6
@freakonometrics 5
7. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Nonparametric estimation (and Borders)
with Gery Geenens & Davy Pandaveine Copula Density Estimation and Probit
Trransform, (Bernoulli, 2015)
From a n-i.i.d. samepl {xi, yi} define the nor-
malized pseudo-sample {(si, ti)}
ui = Φ−1
(ui) = Φ−1
(FX(xi)) and vi = Φ−1
(vi)
fST (s, t) =
1
n|HST |1/2
n
i=1
K H
−1/2
ST
s − si
t − ti
.
c(τ)
(u, v) =
fST (Φ−1
(u), Φ−1
(v))
φ(Φ−1(u))φ(Φ−1(v))
is the so-called naive estimator...
c~(τ2)
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
1.5
1.5
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1
1.25
1.25
1.5
1.5
2
2
4
c^
β
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
1.5
1.5
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
0.25
0.25
0.25 0.25
0.5
0.5
0.75
0.75
0.75
1
1
1
1
1
1.25
1.25
1.25
1.25
1.25
1.5
1.5
2
2
2
4
c^
b
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
1.5
1.5
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
1.5
1.5
2
2
c^
p
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
1.5
1.5
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
0.25
0.25
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1
1.25
1.25
1.25
1.25
1.5
1.5
1.5
2
2
4
@freakonometrics 7
8. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Nonparametric estimation (and Borders)
with Gery Geenens & Davy Pandaveine Copula Density Estimation and Probit
Trransform, (Bernoulli, 2015)
... with possible ameliorations.
One can derive asymptotic normality
√
nh2 ˜c∗(τ,2)
(u, v) − c(u, v) − h4
B(u, v)
L
→ N 0, σ(2)
2
(u, v) as n → ∞,
where
B(u, v) =
b(2)(u, v)
φ(Φ−1(u)) · φ(Φ−1(v))
Application: LOSS-Alae dataset.
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
c~(τ2)
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1
1.25
1.25
1.5
1.5
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
c^
β
Loss (X)
ALAE(Y)
0.25
0.25
0.25 0.25
0.5
0.5
0.75
0.75
0.75
1
1
1
1
1
1.25
1.25
1.25
1.25
1.25
1.5
1.5
1.5
2
2
2
4
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
c^
b
Loss (X)
ALAE(Y)
0.25
0.25
0.5
0.5
0.75
0.751
1
1.25
1.25
1.5
1.5
2
2
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
c^
p
Loss (X)
ALAE(Y)
0.25
0.25
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1
1.25
1.25
1.25
1.25
1.5
1.5
1.5
2
2
4
@freakonometrics 8
9. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Fondamental Results’ Multivariate Risk Aversion
with Alfred Galichon and Marc Henry, Multivariate Local Utility, (MOR, 2015)
Machina (1982) R has a local utility representation if there is UP such that
R(P) − R(Pε) = − UP(x)d(P − Pε)(x) + o( P − Pε ),
i.e. UP is Fréchet derivative of R in P.
Ex: Entropic measure, R(P) = −
1
α
EP(e−αX
), then UP(x) =
1
α
e−αx
EP(e−αX)
.
Ex: Distorted measure R(P) =
1
0
F−1
X (u)ϕ(u)du, then UP(x) =
x
ϕ(FX(z))dz.
R is Schur-concave if and only if UP is concave, ∀P ∈ L2
.
Let X0 ∼ P and X1 ∼ Q such that E(X1|X0) = X0. There exists (Xt)t∈[0,1]
(martingale interpolation) such that X0 = X0, X1 = X1, with dXt = ΣtdBt,
and R(Xs) ≤ R(Xt) for all s < t.
@freakonometrics 9
10. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Applied Mathematics’ Causality and Time Series
with David Sibaï Hurst/Gumbel and Floods, (Environmentrics 2008) or Heat
Waves, (CC 2011) or with Marilou Durand Dynamics of Earthquakes, (JS 2015)
q
q
q
q
q
q
q
q
q
q
q
q q
q q
q
q
q
q
q
q
q
q
q
q
q q
q
q
q
q
q
q
q
q q
q
q q q
q
q
q q
q
q
q
q
q
q
q
q q
q
q
q
q
q q q
q
q
101520
Temperaturein°C
juil. 02 juil. 12 juil. 22 août 01 août 11 août 21 août 31
q
q
q
q
q q
0 1 2 3 4 5
010203040506070
Number of large earthquake (Magn.>7) per year, 1,000 km from Tokyo
Frequency(in%)
q Benchmark
Gamma−Pareto
Weibull−Pareto
q
q
q
q
q
q
q
q
q
q
q
q q q q q
0 5 10 15
05101520
Number of large earthquake (Magn.>7) per decade, 1,000 km from Tokyo
Frequency(in%)
q Benchmark
Gamma−Pareto
Weibull−Pareto
0 50 100 150 200
0.00.20.40.60.81.0
Distribution function of the period of return
Years before next heat wave
4consecutivedaysexceeding24degrees
GARMA + Gaussian noise
ARMA + t noise
ARMA + Gaussian noise
0 50 100 150 200
0.00.20.40.60.81.0
Distribution function of the period of return
Years before next heat wave
11consecutivedaysexceeding19degrees
GARMA + Gaussian noise
ARMA + t noise
ARMA + Gaussian noise
q
q
q q q q
0 1 2 3 4 5
020406080
Number of large earthquake (Magn.>7.5) per year, 1,000 km from Tokyo
Frequency(in%)
q Benchmark
Gamma−Pareto
Weibull−Pareto
q
q
q
q
q
q
q q q q q q q q q q
0 5 10 15
0102030
Number of large earthquake (Magn.>7.5) per decade, 1,000 km from Tokyo
Frequency(in%)
q Benchmark
Gamma−Pareto
Weibull−Pareto
@freakonometrics 10
11. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Applied Mathematics’ Causality and Time Series
with Mathieu Boudrault Multivariate INAR, (2012)
Inspired by Steutel & van Harn (1979) define a mul-
tivariate thinning operator,
[P ◦ N]i =
d
j=1
pi,j ◦ Nj, with p ◦ N =
N
k=1
Yk
where Y1, Y2, · · · are i.id. B(p)’s. A MINAR is
Xt = P ◦ Xt−1 + εt
where εt are i.id. Poisson random vectors.
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Granger Causality test, 3 hours
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Granger Causality test, 6 hours
See also joint work with M Toledo Bastos & Dan Mercea Onsite & Online Protest
Activity, (JC, 2015).
@freakonometrics 11
12. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Applied Mathematics’ Applications of Game Theory
with Benoit Le Maux Natural Catastrophes and Cooperation, (JPE, 2014)
E[u(ω − X)]
no insurance
≤ E[u(ω − α−l + I)]
insurance=V
with indeminty I(·) can be function of the propor-
tion of the population claiming a loss.
With limited liability
V = U(−α)−
1
0
x[U(−α)−U(−α− +I(x))]f(x)dx
See also work with Stéphane Mussard Income Inequality Games (JEI, 2011) and
with Romuald Élie .
@freakonometrics 12
13. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
‘Applied Mathematics’ Actuarial Science
Books on Mathématiques de l’Assurance
Non-Vie with Michel Denuit and book
on Computational Actuarial Science.
Articles on insurance models, Insurability of Climate Risk (GP 2009), on Claims
Reserving, micro vs. macro with Mathieu Pigeon (Risks, 2016) or on Bonus-Malus
Systems with Arthur David & Romuald Élie (2016).
@freakonometrics 13
14. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
Popular Writing / Articles en Français
@freakonometrics 14
15. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
On-going work
Enora Betz , Pierre-Yves Geoffard & Julien Tomas Bodily Injury Claims in France:
Court or Negociated Settlement ? »*
Emmanuel Flachaire & Magali Fromont Machine Learning & Econometrics
Alfred Galichon & Lucas Vernet Min-Cost Flows Models in Economics »*
Amadou Barry & Karim Oualkacha Quantile and Expectile Regression for random
effects model »*
Antoine Ly Classification with Unbalanced Samples »*
Ewen Gallic & Olivier Cabrignac Mortality in France and Familal Dependencies,
from Genealogical Data »*
Arnaud Goussebaile Insurance of Natural Catastrophes, Risk and Ambiguity »*
Ndéné Ka, Stéphane Mussard & Oumar Ndiaye Gini Regression and
Heteroskedasticity »*
@freakonometrics 15
16. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
« Min-Cost Flow Models in Economics*
(source Church (2009))
@freakonometrics 16
17. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
« Min-Cost Flow Models in Economics*
@freakonometrics 17
18. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
« Quantile and Expectile Regression for Random Effects Models*
Quantile, q(α, Y ) = argmin
θ ∈ R
E(rQ
α (Y − θ)) with rQ
α (u) = |α − 1(u ≤ 0)| · |u|.
Empirical version q(α, Y ) = argmin
θ ∈ R
1
n
n
i=1
rQ
α (yi − θ)
Quantile Regression β
Q
(α, y, x) = argmin
β ∈ Rp
1
n
n
i=1
rQ
α (yi − xi
T
β)
see Koenker (2005). Following Newey & Powell (1987) define expectiles as
µ(τ, Y ) = argmin
θ ∈ R
E(rE
τ (Y − θ)) with rE
τ (u) = |τ − 1(u ≤ 0)| · u2
.
Expectile Regression β
E
(τ, y, x) = argmin
β ∈ Rp
1
n
n
i=1
rE
τ (yi − xi
T
β) .
Properties of estimators in the context of panel data, (yi,t, xi,t).
@freakonometrics 18
19. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
« Quantile and Expectile Regression for Random Effects Models
@freakonometrics 19
20. Arthur CHARPENTIER, HdR: Contribution à l’étude de la dépendance
« Conclusion (?)
Work in ‘fundamental’ results
as well as applications
(insurance, finance, economics, climate).
Work with researchers in applied
mathematics and economics
involving students
(undergraduate, graduate, PhD, post-doc)
Currently involved in projects
• ANR, multivariate inequalities
• ACTINFO research chair
@freakonometrics 20
