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On Modeling Insurance Claims using Copulas

Erntell, Filip (2013) MASM01 20132
Mathematical Statistics
Abstract (Swedish)
In this master's thesis, a copula approach is used to model the number of claims
made by a customer holding three insurances. It is important for insurance companies
to have good models for the risk proles of their customers, and the number of
claims is a key element in calculating the expected cost for the company. Using copulas,
multivariate distribution functions are allowed to have any desired marginal
distributions and many dierent dependence structures, as these can be chosen
separately.
The data used consists of the number of claims made by 74 770 unique customers
during one year. Dierent count data distributions are considered for the onedimensional
marginal distributions, while four Archimedean copulas are tested as
... (More)
In this master's thesis, a copula approach is used to model the number of claims
made by a customer holding three insurances. It is important for insurance companies
to have good models for the risk proles of their customers, and the number of
claims is a key element in calculating the expected cost for the company. Using copulas,
multivariate distribution functions are allowed to have any desired marginal
distributions and many dierent dependence structures, as these can be chosen
separately.
The data used consists of the number of claims made by 74 770 unique customers
during one year. Dierent count data distributions are considered for the onedimensional
marginal distributions, while four Archimedean copulas are tested as
models for the dependence structure. To estimate the parameters of the nal model,
full maximum likelihood is used, for which new implementations adapted to discrete
data were created.
2-tests and likelihood ratio tests determined that negative binomial distribution
and zero-in
ated Delaporte distribution were the best distributions for the onedimensional
marginals, while Cramer-von Mises method and Kendall's Cramer-von
Mises method, using a parametric bootstrap, together with Akaike's Information
Criterion, suggested Clayton copula to be the most suitable.
The obtained model is compared to the empirical values and to investigate how
well the model ts for dierent years, it is also tted to the corresponding data from
the following year. The model provides a good t both compared to the empirical
values for the year used for inference as well as for the year used for validation.
However, the t is strongly in
uenced by the values in the lower tail.
Keywords: Insurances, Copulas, Count data, Negative binomial distribution, Delaporte
distribution, Full maximum likelihood, Goodness of t. (Less)
Please use this url to cite or link to this publication:
author
Erntell, Filip
supervisor
organization
course
MASM01 20132
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
4114190
date added to LUP
2013-10-22 12:24:12
date last changed
2013-10-22 12:24:12
@misc{4114190,
  abstract     = {In this master's thesis, a copula approach is used to model the number of claims
made by a customer holding three insurances. It is important for insurance companies
to have good models for the risk proles of their customers, and the number of
claims is a key element in calculating the expected cost for the company. Using copulas,
multivariate distribution functions are allowed to have any desired marginal
distributions and many dierent dependence structures, as these can be chosen
separately.
The data used consists of the number of claims made by 74 770 unique customers
during one year. Dierent count data distributions are considered for the onedimensional
marginal distributions, while four Archimedean copulas are tested as
models for the dependence structure. To estimate the parameters of the nal model,
full maximum likelihood is used, for which new implementations adapted to discrete
data were created.
2-tests and likelihood ratio tests determined that negative binomial distribution
and zero-in
ated Delaporte distribution were the best distributions for the onedimensional
marginals, while Cramer-von Mises method and Kendall's Cramer-von
Mises method, using a parametric bootstrap, together with Akaike's Information
Criterion, suggested Clayton copula to be the most suitable.
The obtained model is compared to the empirical values and to investigate how
well the model ts for dierent years, it is also tted to the corresponding data from
the following year. The model provides a good t both compared to the empirical
values for the year used for inference as well as for the year used for validation.
However, the t is strongly in
uenced by the values in the lower tail.
Keywords: Insurances, Copulas, Count data, Negative binomial distribution, Delaporte
distribution, Full maximum likelihood, Goodness of t.},
  author       = {Erntell, Filip},
  language     = {eng},
  note         = {Student Paper},
  title        = {On Modeling Insurance Claims using Copulas},
  year         = {2013},
}