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Insurance Loss Reserving

Bjarnason, Theodor and Sjögren, Marcus (2014) FMS820 20141
Mathematical Statistics
Abstract (Swedish)
The concept of run-o triangles is widely used within the actuarial
eld. Its purpose is to estimate Incurred But Not Reported claims for
insurance portfolios, in order to set appropriate reserves that are in
compliance with regulatory requirements as well as the company's risk
appetite. In this thesis, a parametric approach is proposed, where the
portfolios are modeled using non-stationary distributions. The nonstationarity
is able to account for various dependencies arising within
the run-o triangle. In order to handle negative values, the families
within the Generalized Extreme Value distribution have been applied.
The ndings are then benchmarked by comparing the method to a
non-parametric Chain Ladder bootstrap approach. Using... (More)
The concept of run-o triangles is widely used within the actuarial
eld. Its purpose is to estimate Incurred But Not Reported claims for
insurance portfolios, in order to set appropriate reserves that are in
compliance with regulatory requirements as well as the company's risk
appetite. In this thesis, a parametric approach is proposed, where the
portfolios are modeled using non-stationary distributions. The nonstationarity
is able to account for various dependencies arising within
the run-o triangle. In order to handle negative values, the families
within the Generalized Extreme Value distribution have been applied.
The ndings are then benchmarked by comparing the method to a
non-parametric Chain Ladder bootstrap approach. Using Value-at-
Risk and Tail Value-at-Risk measures, the aggregated reserve is then
estimated through Monte Carlo simulations by applying elliptical copulas,
where the eects from dependence between portfolios are studied.
The method is applied on data provided by a Swedish reinsurer, for its
portfolios Aviation, Marine and Property. The implementation of the
method conveys the impact of model risk and the importance of accurate
parameter estimation, otherwise resulting in unrealistic projections.
Additionally, dependence for dierent copulas, tail dependence
in particular, is proven to have considerable eect for aggregated loss
reserving.
Keywords: Run-o triangle, IBNR, Non-stationary marginal distributions,
Elliptical copulas, Generalized Extreme Value distribution,
Value at Risk, Maximum Likelihood Estimation, Chain Ladder. (Less)
Please use this url to cite or link to this publication:
author
Bjarnason, Theodor and Sjögren, Marcus
supervisor
organization
alternative title
A Run-Off Triangle Approach Using Copulas With Non-Stationary Marginal Distributions
course
FMS820 20141
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
4588556
date added to LUP
2014-08-18 11:15:19
date last changed
2014-08-18 11:15:19
@misc{4588556,
  abstract     = {{The concept of run-o triangles is widely used within the actuarial
eld. Its purpose is to estimate Incurred But Not Reported claims for
insurance portfolios, in order to set appropriate reserves that are in
compliance with regulatory requirements as well as the company's risk
appetite. In this thesis, a parametric approach is proposed, where the
portfolios are modeled using non-stationary distributions. The nonstationarity
is able to account for various dependencies arising within
the run-o triangle. In order to handle negative values, the families
within the Generalized Extreme Value distribution have been applied.
The ndings are then benchmarked by comparing the method to a
non-parametric Chain Ladder bootstrap approach. Using Value-at-
Risk and Tail Value-at-Risk measures, the aggregated reserve is then
estimated through Monte Carlo simulations by applying elliptical copulas,
where the eects from dependence between portfolios are studied.
The method is applied on data provided by a Swedish reinsurer, for its
portfolios Aviation, Marine and Property. The implementation of the
method conveys the impact of model risk and the importance of accurate
parameter estimation, otherwise resulting in unrealistic projections.
Additionally, dependence for dierent copulas, tail dependence
in particular, is proven to have considerable eect for aggregated loss
reserving.
Keywords: Run-o triangle, IBNR, Non-stationary marginal distributions,
Elliptical copulas, Generalized Extreme Value distribution,
Value at Risk, Maximum Likelihood Estimation, Chain Ladder.}},
  author       = {{Bjarnason, Theodor and Sjögren, Marcus}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Insurance Loss Reserving}},
  year         = {{2014}},
}