## Stochastic chain-ladder models in nonlife insurance

##### Sammendrag

This thesis examines the stochastic models which reproduce chain-ladder estimates used in
reserve estimation for nonlife insurance. The chain-ladder method provides no information
regarding the variability of the outcome, thereby adding uncertainty to future claim
estimations. Prediction errors can be found using a variety of stochastic chain-ladder models,
but the different models are based on different assumptions. The relationship between some
of these models was explored, and it was demonstrated how the models are defined for a runoff
triangle of insurance claims. Two of these models, Mack’s model and the normal
approximation to the negative binomial model, were applied to a data set consisting of auto
liability insurance claims. This was done in order to find the prediction error of their chain
ladder estimates, as well as verify their ability to handle negative values. The two models
used in the analysis were found to produce nearly identical prediction errors, and both were
able to handle negative insurance claims, which were present in the data set. A number of
similarities were found between the models, to the degree that the normal approximation to
the negative binomial model should be considered as underlying Mack’s model. However,
since it is based on a generalized linear model, the normal approximation to the negative
binomial model offers greater flexibility in applied calculations than Mack’s model.

##### Utgiver

The University of Bergen##### Samlinger

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