Ιδιότητες της από κοινού κατανομής του χρόνου χρεοκοπίας, του πλεονάσματος ακριβώς πριν τη χρεοκοπία και του ελλείμματος κατά τη χρεοκοπία
Some properties of the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
Μετζάκη, Αικατερίνη Β.
In the present Dissertation, we study the joint distribution of the time of ruin, the surplus before ruin and the deficit at ruin. The object of view is to give explicit formulas of the density functions of the random variables in both, classical and renewal, models of ruin theory. In particular, we are going to examine the joint distribution of the surplus before ruin and the deficit at ruin for positive force of interest, for the classical model, moreover for the renewal, in a more general form, while the distribution of interclaim times and claims are phase - type. Also, we are going to be involved in the study of the renewal model, when there is zero forse of interest, in explicitly occasions, while the distribution of interclaim times, is Erlang (2,2), generilised Erlang and also phase- type (2). In each case, we give examples, to illustrate the derivation of the functions we are interested in, to highlight important comments on the continuation of the functions, as well as to compare the two models of ruin theory.