Μοντελοποίηση αναλογιστικών δεδομένων απώλειας με σύνθετα μοντέλα
Modelling actuarial data using composite models
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Σύνθετα μοντέλαAbstract
The analysis and modeling of losses in the insurance sector is a fundamental subject
of Actuarial Science and Applied Statistics. In many cases, losses show strong
heterogeneity, with different statistical behavior in small and large losses. Specifically,
loss data are often characterized by a large concentration of small or medium values,
while at the same time they include extreme observations that can significantly affect
their distribution.
For the better description of this dual nature of the data, the use of composite models
has been proposed, which combine different probability distributions depending on the
region (interval) of the size of the losses. Typically, a distribution such as the Lognormal
or Weibull is applied to approximate the “normal” losses, while for extreme values other
distributions are used, such as the Pareto distribution, also in accordance with extreme
value theory.
A critical element in the construction of a composite model is the selection of the
threshold separating the two distributions, as well as their proper normalization through
truncated distributions, so that the final model corresponds to a probability density.
In the present paper, the application of such models to loss data from the actuarial
field is studied, with the aim of accurately describing the overall distribution of losses. In
Chapter 1, the theoretical basis of composite distributions and the methods for estimating
their parameters are presented. In Chapter 2, the main composite models that have been
studied in the literature are presented, while in Chapter 3, the application of these models
to real data is examined (e.g. the Danish fire losses data). Particular emphasis is placed on
the appropriate selection of the threshold, as well as on the statistical estimation of the
relative weights of the individual components of the model.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διαχείριση ΚινδύνωνDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
146Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα