Στοχαστικές διαδικασίες πλεονάσματος με δίπλευρα άλματα
Stochastic surplus processes with two-sided jumps
Κροκιδάς, Νικόλαος - Ερμής
KeywordsΣτοχαστικές διαδικασίες ; Διαχείριση κινδύνου ; Διαχείριση χαρτοφυλακίου ; Συναρτήσεις ; Δίπλευρα άλματα ; Πλεόνασμα ; Χρεοκοπία ; Στατιστική ανάλυση
The purpose of this Thesis is the study of various stochastic processes of surplus with twosided jumps happening both in distinct and continuous time, with or without the presence of a random diffusion term which is described by a stochastic Brownian motion. The upward jumps represent the random gain sizes while the downward jumps represent the claim sizes of the portflolio. Therefore, these surplus models include as special cases equivalent models of Classical Ruin Theory. Considering various distributions for the sizes of the two sided-jumps, as well as for the time between risk appearances, various ruin measures will be studied through the expected Gerber- Shiu discounted penalty function as well as asymptotic results will be given for the ruin probability.