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master's thesis
Brownovo gibanje u osiguranju
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:649955
Aničić, Ena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Aničić, E. (2023). Brownovo gibanje u osiguranju (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:649955

Aničić, Ena. "Brownovo gibanje u osiguranju." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:649955

Aničić, Ena. "Brownovo gibanje u osiguranju." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:649955

Aničić, E. (2023). 'Brownovo gibanje u osiguranju', Master's thesis, University of Zagreb, Faculty of Science, accessed 06 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:649955

Aničić E. Brownovo gibanje u osiguranju [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 06] Available at: https://urn.nsk.hr/urn:nbn:hr:217:649955

E. Aničić, "Brownovo gibanje u osiguranju", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:649955

Metadata
TitleBrownovo gibanje u osiguranju
Title (english)Brownian motion in insurance
AuthorEna Aničić
MentorZoran Vondraček (mentor)
Committee memberVanja Wagner (predsjednik povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberGoran Muić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavali smo politiku reosiguranja i potražnje za priljevima novaca s ciljem očuvanja poslovanja tvrtke i spašavanja iste od propasti. Cilj modela bio je ustvrditi trenutke u kojima je potrebno zatražiti priljev novaca te njihov iznos, pronaći optimalnu razinu reosiguranja (za oba oblika reosiguranja) te funkciju vrijednosti koja prati troškove firme i minimizira ih. Optimalna funkcija vrijednosti pronađena je eksplicitno pomoću kvazi-varijacijskih nejednakosti i radi se o eksponencijalnoj funkciji. Trenuci u kojima je potrebno zatražiti priljeve novaca su upravo oni u kojima dolazi do propasti poslovanja (pričuva je jednaka nuli). Iznosi priljeva novaca kao i optimalna razina reosiguranja su konstante. Time je optimalna politika koja kontrolira pričuvu modelirana difuzijskim procesom sa skokovima gdje je pričuvni proces Brownovo gibanje s konstantnim driftom i konstatnim skokovima napravljenima u trenucima propasti poslovanja.
Abstract (english)
In this paper, we studied an optimal reinsurance policy as well as the optimal policy of cash-injection calls. The presented model establishes the moments in which it is necessary to request cash injections and determines their amount, it also finds the optimal level of reinsurance (for both forms of reinsurance) and the value function that minimizes the cost. The optimal value function is found explicitly using QVI and is an exponential function. Cash-injections are optimally called at the moment of ruins (surplus is equal to zero) and their amount was found to be constant. The optimal level of reinsurance is also found to be constant. Thus, the optimal policy that controls surplus process was modeled by jumpdiffusion process and the surplus process became a Brownian motion with a constant drift and constant jumps at the times of ruin.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:649955
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 conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-03-21 13:44:09