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A Copula Approach to Modeling Insurance Claims

Hage, Madeleine (2013) FMS820 20131
Mathematical Statistics
Abstract (Swedish)
It is crucial for the insurance business to create risk profiles for
their customers to be able set a fair price for their insurances. This
thesis presents an alternative method for measuring the dependence
between the numbers of claims made by a customer holding two insurances.
The group of insurance holders consisted of 74770 unique customers
holding at least two insurances during one year. The method uses copulas
to model the dependence between the numbers of claims made in each
insurance. An advantage using copulas to model the dependence is that
the margins and the dependence structure can be modeled separately. The
copulas used in the analysis were four Archimedean copulas namely
Clayton, Frank, Gumbel and Ali-Mikhail- Haq.... (More)
It is crucial for the insurance business to create risk profiles for
their customers to be able set a fair price for their insurances. This
thesis presents an alternative method for measuring the dependence
between the numbers of claims made by a customer holding two insurances.
The group of insurance holders consisted of 74770 unique customers
holding at least two insurances during one year. The method uses copulas
to model the dependence between the numbers of claims made in each
insurance. An advantage using copulas to model the dependence is that
the margins and the dependence structure can be modeled separately. The
copulas used in the analysis were four Archimedean copulas namely
Clayton, Frank, Gumbel and Ali-Mikhail- Haq. These copulas were chosen
for their simple explicit expressions and variety in dependence structure.

A flag has to be raised regarding the fact that the margins were
discrete and the largest part of applied copula theory handles
continuous margins. This led to complications in the modeling that
were not expected. The marginal parameters were estimated using
ML-method and a χ2-test decided that the negative binomial distribution
respectively the zero-inflated negative binomial distribution were the
best fits for the insurances. Regarding the copula, the parameter was
estimated using inverse Kendall's tau. By performing a parametric
bootstrap using Craḿer von Mises method the Gumbel copula was shown
to provide the best fit.

When a bivariate distribution was obtained from the model, it was
compared to the empirical counterpart. Conditional distributions and
conditional expected values were calculated from the bivariate model and
they were compared to their empirical equivalent. The conclusion was
that the model provided an overall good fit but the best fit was in the
lower tail. (Less)
Please use this url to cite or link to this publication:
author
Hage, Madeleine
supervisor
organization
course
FMS820 20131
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
3683827
date added to LUP
2013-04-22 13:58:43
date last changed
2013-04-23 03:47:49
@misc{3683827,
  abstract     = {It is crucial for the insurance business to create risk profiles for
their customers to be able set a fair price for their insurances. This
thesis presents an alternative method for measuring the dependence
between the numbers of claims made by a customer holding two insurances.
The group of insurance holders consisted of 74770 unique customers
holding at least two insurances during one year. The method uses copulas
to model the dependence between the numbers of claims made in each
insurance. An advantage using copulas to model the dependence is that
the margins and the dependence structure can be modeled separately. The
copulas used in the analysis were four Archimedean copulas namely
Clayton, Frank, Gumbel and Ali-Mikhail- Haq. These copulas were chosen
for their simple explicit expressions and variety in dependence structure.

A flag has to be raised regarding the fact that the margins were
discrete and the largest part of applied copula theory handles
continuous margins. This led to complications in the modeling that
were not expected. The marginal parameters were estimated using
ML-method and a χ2-test decided that the negative binomial distribution
respectively the zero-inflated negative binomial distribution were the
best fits for the insurances. Regarding the copula, the parameter was
estimated using inverse Kendall's tau. By performing a parametric
bootstrap using Craḿer von Mises method the Gumbel copula was shown
to provide the best fit.

When a bivariate distribution was obtained from the model, it was
compared to the empirical counterpart. Conditional distributions and
conditional expected values were calculated from the bivariate model and
they were compared to their empirical equivalent. The conclusion was
that the model provided an overall good fit but the best fit was in the
lower tail.},
  author       = {Hage, Madeleine},
  language     = {eng},
  note         = {Student Paper},
  title        = {A Copula Approach to Modeling Insurance Claims},
  year         = {2013},
}