Στοχαστικές ανελίξεις Levy στη θεωρία χρεοκοπίας: μελέτη της συνάρτησης των Gerber - Shiu
Stochastic Levy processes in ruin theory: study of the Gerber - Shiu function
Κυνηγός, Άγγελος Χ.
SubjectΚίνδυνος (Ασφάλεια) -- Μαθηματικά μοντέλα ; Ασφάλιση -- Μαθηματικά ; Levy processes ; Risk (Insurance) -- Mathematical models ; Insurance -- Mathematics
During the management of insurance claims portfolios, volatilities are often been observed with respect to the heights of the collected premiums or/ and with respect to the heights of the paid claims. In these cases, in order to study the stochastic surplus process of the portfolio, this randomness is studied considering the existence of a diffusion factor described by the Wiener process. Then, the classic model of the risk theory is reduced to a Levy process. The purpose of this thesis is the study of various risk measures of an appropriate Levy process as a stochastic surplus process. This will initially be a comprehensive study of the Spectrally Negative Levy Processes and their corresponding Scale Functions. It will be shown that through them a generalized function of Gerber - Shiu can be studied. In addition, it will be shown that a renewal risk model with arrival interclaim times follows a Coxian distribution, for which the stochastic surplus process is perturbed by a spectrally negative Levy process.