Procesi obnavljanja u teoriji rizika

master's thesis

• Author: Zorana Lubina
• Mentor: Zoran Vondraček (mentor)
• Committee member: Zoran Vondraček (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu prezentirani su osnovni koncepti teorije rizika koja modelira dva izvora neizvjesnosti neživotnog osiguranja: koliko će šteta osiguranik prijaviti i koliki su iznosi tih šteta. U skladu s time, definirani su proces ukupnog broja šteta i proces ukupnog iznosa šteta. Zajedno, ta dva procesa čine sastavni dio procesa rizika koji prati odnos uplaćenih premija i isplaćenih šteta. Rad je podijeljen u pet poglavlja. U prva dva poglavlja opisana su osnovna svojstva matematičkih modela za proces ukupnog broja šteta - homogenog Poissonovog procesa i procesa obnavljanja. U trećem poglavlju dan je pregled distribucija iznosa štete, pri čemu je poseban naglasak stavljen na distribucije teškog repa - regularno varirajuće i subeksponencijalne distribucije. U četvrtom poglavlju objašnjena su osnovna svojstva modela za proces ukupnog iznosa šteta - Cramér-Lundbergovog modela i modela obnavljanja. Dio poglavlja posvećen je i određivanju distribucije ukupnog iznosa šteta do određenog trenutka \(t\). Posljednje poglavlje prikazuje fundamentalne rezultate teorije propasti čiji je glavni fokus proces rizika.

Abstract (english)

This thesis presents the basic concepts of risk theory that models two sources of non-life insurance uncertainty: how many claims an insured person will report and what are the amounts of those claims. Accordingly, claim number process and total claim amount process are defined. Together, these two processes form a constitutive part of the risk process that monitors the relation between premiums and claims paid. The paper is divided into five chapters. The first two chapters describe the basic properties of the mathematical models for the claim number process - homogeneous Poisson process and renewal process. The third chapter provides an overview of the claim size distributions with particular emphasis on heavy-tailed distributions - regularly varying and subexponential distributions. The fourth chapter explains the basic model properties for the total claim amount process - Cramér-Lundberg model and renewal model. Part of the chapter is also devoted to deter- mining the distribution of the total claim amount up to a certain moment \(t\). The last chapter presents the fundamental results of the ruin theory whose main focus is the risk process.

• Keywords: teorija rizika; neživotno osiguranje; teorija propasti
• Keywords (english): risk theory; non-life insurance; ruin theory
• Language: croatian
• URN:NBN: urn:nbn:hr:217:703675
• 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; Embargo expiration date: 2022-09-15
• Created on: 2020-09-15 11:35:41