Vjerojatnost propasti

master's thesis

• Author: Iva Brnić
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovoga diplomskog rada bio je definirati osnovne pojmove vezane uz vjerojatnost propasti osiguravajućeg društva i dokazati neke ključne rezultate za Poissonove procese, kao što su Pollaczek-Khinchinova formula, Lundbergova nejednakost, Cramer-Lundbergova aproksimacija te izraz za vjerojatnost propasti kada isplate dolaze iz eksponencijalne distribucije. Neke od navedenih rezultata poopćili smo i za slučaj miješanih Poissonovih procesa. Također smo analizirali ovisnost vjerojatnosti propasti o parametrima modela, distribuciji isplata i distribuciji intenziteta miješanog Poissonovog procesa. Naposljetku smo opisali jedan način procjene vjerojatnosti propasti te razmotrili preciznost dobivenih procjena.

Abstract (english)

The aim of this thesis was to define the main concepts connected with the probability of ruin and to prove some of the key results for Poisson processes such as the Pollaczek-Khinchine formula, the Lundberg inequality, the Cramer-Lundberg approximation and the expression for the probability of ruin when the claims are exponentially distributed. We generalized some of those results for the mixed Poisson case as well. We also analyzed the dependence of the probability of ruin on the model parameters, the distribution of the claims and the distribution of the intensity of the mixed Poisson process. Finally, we described how to estimate the probability of ruin and discussed whether the estimation is accurate.

• Keywords: vjerojatnost propasti osiguravajućeg društva; Poissonov proces; Pollaczek-Khinchinova formula; Lundbergova nejednakost; Cramer-Lundbergova aproksimacija
• Keywords (english): the probability of ruin; Poisson processes; the Pollaczek-Khinchine formula; the Lundberg inequality; the Cramer-Lundberg approximation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:014126
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-03 13:27:05