Procesi obnavljanja u teoriji rizika

Urošev, Siniša (2014) Procesi obnavljanja u teoriji rizika. Diploma thesis, Faculty of Science > Department of Mathematics.

[img]
Preview
PDF
Language: Croatian

Download (623kB) | Preview

Abstract

Risk theory is a synonym for non-life insurance mathematics. It deals with modeling of claims that arrive in an insurance business and risk valuation of loss in portfolio. The main goal of this paper is to introduce basic concepts in risk theory which could model real-life situations. We study renewal processes which could be used to model arrival of claims. Some important results in renewal theory are listed and Poisson process is of special interest. Next we observe the total claim amount processes which could be used to model claims which insurance company discharges. Like in renewal theory, some important results are listed with special interest in compound Poisson process. The biggest part of this work is dedicated to ruin theory and Sparre Andersen model. The object of interest is time of ruin which is defined as the first time when accumulated claims surpass premium. We derive a closed-form representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. For general model, algorithm based on Monte Carlo simulation is proposed. In this work it could also be found some basic results on Lévy processes and probability theory which are used in this paper.

Item Type: Thesis (Diploma thesis)
Supervisor: Vondraček, Zoran
Date: 2014
Number of Pages: 54
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 28 Aug 2015 12:26
Last Modified: 28 Aug 2015 12:26
URI: http://digre.pmf.unizg.hr/id/eprint/4200

Actions (login required)

View Item View Item