Bayesova metoda u neživotnom osiguranju

master's thesis

• Author: Katja Kegel
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kroz ovaj rad je prikazano kako se Bayesova statistika i tehnike Markovljevog lanca Monte Carlo koriste u nepodmirenim obvezama u jednoj osiguravajućoj kući. Upoznali smo se sa osnovnim pojmovima Bayesove statistike i najvažnijim terminom poznatijim pod nazivom Bayesov teorem. Uz to, upoznali smo se svojstvima Markovljevog lanca te tehnikama Markovljevog lanca Monte Carlo među kojima su i dva algoritma poznatija pod imenima Metropolis-Hasting algoritam i Gibbsovo sempliranje. Na temelju zadanih podataka, promotrili smo i analizirali dva modela, logaritamski i eksponencijalni, te odabrali koji od dva navedena najbolje odgovaraju našim podacima. Za odabir boljeg modela koristili smo grafičku analizu i kriterij devijantnosti (DIC) te je kao bolji odabran logaritamski model. Na kraju, koristeći MCMC metode procijenili smo buduće iznose šteta koji moraju biti plaćeni, kao i nedostajuće vrijednosti te još jednom potvrdili kako je odabrani logaritamski model dao poprilično zadovoljavajuće rezultate.

Abstract (english)

Through this dissertation, we have shown how one can use Bayesian statistics and Markov Chain Monte Carlo techniques in outstanding liabilities of an insurance company. We met with the basic concepts of Bayesian statistics and the most important term known as the Bayes' theorem. In addition, we introduced the properties of Markov chain techniques and Markov chain Monte Carlo including the two algorithms also known as Metropolis-Hastings algorithm and Gibbs sampling. Based on the given data, we observed and analyzed the two models, lognormal and exponential, and have been able to select the one fitting the data better. To select a better model, we used graphical analysis and deviance criterion (DIC) and lognormal model was selected as the one that fits the data better. Finally, using MCMC methods we assessed future claim amounts that must be paid, as well as missing values, and once again we confirmed that the selected lognormal model gave us quite satisfactory results.

• Keywords: Bayesova statistika; Markovljev lanac; Markovljevi lanci; Monte Carlo tehnike; Bayesov teorem; Metropolis-Hasting algoritam; Gibbsovo sempliranje; logaritamski model; eksponencijalni model; MCMC metoda
• Keywords (english): Bayesian statistics; Markov chain; Monte Carlo techniques; Bayes' theorem; Metropolis-Hastings algorithm; Gibbs sampling; lognormal model; exponential model; MCMC method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:285336
• Study programme: Title: Mathematical Statistics; 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: Access restricted to students and staff of home institution
• Created on: 2019-02-08 10:45:53