  The existence of large and extreme claims of a non-life insurance portfolio
influences the ability of (re)insurers to estimate the reserve. The excess
over-threshold method provides a way to capture and model the typical behaviour
of insurance claim data. This paper discusses several composite models with
commonly used bulk distributions, combined with a 2-parameter Pareto
distribution above the threshold. We have explored how several threshold
selection methods perform when estimating the reserve as well as the effect of
the choice of bulk distribution, with varying sample size and tail properties.
To investigate this, a simulation study has been performed. Our study shows
that when data are sufficient, the square root rule has the overall best
performance in terms of the quality of the reserve estimate. The second best is
the exponentiality test, especially when the right tail of the data is extreme.
As the sample size becomes small, the simultaneous estimation has the best
performance. Further, the influence of the choice of bulk distribution seems to
be rather large, especially when the distribution is heavy-tailed. Moreover, it
shows that the empirical estimate of $p_{\leq b}$, the probability that a claim
is below the threshold, is more robust than the theoretical one.
