Linearna regresija u aktuarstvu

master's thesis

• Author: Paula Škiljan
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-12, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučili smo primjene linearne regresije u aktuarstvu. Prvi dio obuhvaća teoriju potrebnu za razumijevanje sadržaja: formu i prilagodbu modela, nužne uvjete za valjanost modela te metode testiranja relevantnih svojstava. Dodatno smo promotrili dijagnostičke grafove koji su specifični za linearnu regresiju i koji su od velike pomoći pri detaljnijoj analizi prilagodbe modela. Na osnovu dva primjera predviđanja cijene premije osiguranja smo imali priliku vidjeti linearnu regresiju na djelu. Iako linearna regresija nije idealna za dane podatke, nije niti u potpunosti loša. Iz dobivene analize nam je jasno u kojem smjeru bismo dalje trebali ići, tako da je postavljena dobra osnova za daljnji razvoj modela.

Abstract (english)

In this thesis, we have investigated application of linear regression in actuarial science. First part covers the theory necessary for understanding: model description, model fitting methods, model assumptions and methods for testing certain relevant properties. We have additionally considered diagnostic plots specific to linear regression, which are of great help with detailed analysis of the goodness-of-fit. We have investigated the performance of the linear regression based on two examples of the insurance premium prediction. Even though the linear regression is not ideal for the given datasets, it is not very bad either. From the analysis one can see how to proceed and thus the linear model is a good starting point for more complicated models.

• Keywords: linearna regresija; aktuarstvo; premije osiguranja
• Keywords (english): linear regression; actuarial science; insurance premium
• Language: croatian
• URN:NBN: urn:nbn:hr:217:186999
• 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: 2020-06-24 10:36:08