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master's thesis
Bayesova metoda u neživotnom osiguranju
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:285336
Kegel, Katja
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kegel, K. (2014). Bayesova metoda u neživotnom osiguranju (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:285336

Kegel, Katja. "Bayesova metoda u neživotnom osiguranju." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:285336

Kegel, Katja. "Bayesova metoda u neživotnom osiguranju." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:285336

Kegel, K. (2014). 'Bayesova metoda u neživotnom osiguranju', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:285336

Kegel K. Bayesova metoda u neživotnom osiguranju [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:285336

K. Kegel, "Bayesova metoda u neživotnom osiguranju", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:285336

Metadata
TitleBayesova metoda u neživotnom osiguranju
AuthorKatja Kegel
MentorSiniša Slijepčević (mentor)
Committee memberSiniša Slijepčević (predsjednik povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
Committee memberSonja Štimac (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-14, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:285336
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2019-02-08 10:45:53