Approximations for stop-loss reinsurance premiums

Statistical analysis of dependencies within insurance portfolios

“…Such a setup first time was introduced in Albers [1999]. The research was continued with Reijnen's [2003] master thesis, which was partially summarized in Reijnen et al [2005]. The present thesis can be considered as a continuation of that work.…”

“…This is because the basic target of our consideration is the random sum of random variables, the distribution of which is usually far form normal. Moreover, in the previous research, Albers [1999] and Reijnen et al [2005] showed that the tail of the distribution is very sensitive to the dependence effect. It certainly is present everywhere, but in the tail it simply blows up, which can lead to huge risk underestimation.…”

“…In Kaas et al [2001] various types of distributions are described which are often used in the insurance practice. Reijnen et al [2005] contains an overview of the classical and some new assumptions for the claim size modeling. The classical, well-known, candidates for the claim size distribution are the Gamma, Log-normal and Pareto distributions.…”

“…More details will be given in Chapter 3. The same model, in a slightly modified form and with different distributional assumptions appeared later in Reijnen et al [2005]. During our research the model was generalized several times.…”

“…A similar (with the same approach to dependence) model, in a slightly different form and with different distributional assumptions, appeared later in Reijnen et al [2005]. The total aggregate sum of all the claims was presented there as 6) with P (X j = 1) = 1 − P (X j = 0) = q, h = n/g and W ∼ binomial(h, θ).…”