Ο αριθμός των αποζημιώσεων μέχρι τη χρεωκοπία στο ανανεωτικό μοντέλο της θεωρίας κινδύνου
Ματζιώρος, Παναγιώτης Β.
SubjectΔιαχείριση κινδύνου -- Οικονομετρικά μοντέλα ; Διαχείριση κινδύνου -- Στατιστικές μέθοδοι ; Εταιρείες -- Πτώχευση ; Κατανομή (Οικονομική θεωρία)
Within the scope of ruin theory and risk theory nowadays, the description and analysis of the probability distribution, of the number of claims until the time of ruin, can be important, regarding the study and observation of an insurance risk portfolio. In the present dissertation, we study the probability distribution of the number of claims until the ruin, will take place, in the special case of the renewal risk model. For this analysis, we assume that the interarrival time intervals, between the successive claim sizes, follow an Erlang (continuous) distribution (and not the Exponential distribution, as it holds in the simplified case of the classical risk model), and that the individual claim sizes, follow an Exponential distribution. Moreover, apart from the above-mentioned theoretical study, a few indicative charts and diagrams, concerning the analyzed probability distribution of the number of claims until ruin, will be presented and explained, in a separate chapter of this dissertation. These charts, will depict this probability distribution, for special cases of the probabilistic parameters in the renewal risk model, regarding the (continuous) distributions of the interarrival time intervals and the individual claim sizes, which were mentioned above. However, in any case, this master dissertation, does not aim to address the renewal risk model in its full generality, because only the special case of the Erlang distribution is examined and analyzed particularly, regarding the interarrival time intervals of the claims. The other special cases, for the distributions of the interarrival time intervals, in the renewal risk model, have not been studied and analyzed yet, within the scope of modern actuarial bibliography.