Model dvostrukog smanjenja

master's thesis

• Author: Kruno Bartoluci
• Mentor: Hrvoje Šikić (mentor)
• Committee member: Hrvoje Šikić (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U stvaranju financijskih, aktuarskih i medicinskih modela ponekad nije dovoljno promatrati samo vrijeme do završetka određenog stanja već je bitno spoznati i koji je uzrok doveo do završetka tog stanja. Model koji uključuje dvije slučajne varijable, vrijeme do završetka određenog stanja i uzrok završetka tog stanja, naziva se model višestrukog smanjenja. U ovom radu definirani su i objašnjeni osnovni pojmovi modela dvostrukog smanjenja te je analizirano nekoliko modela dvostrukog smanjenja. Ako postoji dovoljno kvalitetnih empirijskih podataka o intenzitetima smanjenja, onda se model dvostrukog smanjenja može predstaviti tablicom dvostrukog smanjenja. U primjeni su modeli dvostrukog smanjenja najčešće dani tablicom dvostrukog smanjenja. U radu je prikazana konstrukcija tablica dvostrukog smanjenja kroz nekoliko primjera. Za svaki od uzroka smanjenja u modelu dvostrukog smanjenja definiran je model jednostrukog smanjenja koji ovisi samo o određenom uzroku smanjenja kako bi se detaljno proučio utjecaj jednog uzroka smanjenja neovisno o drugom uzroku te su pronađene veze između funkcija modela dvostrukog smanjenja i pridruženog mu modela jednostrukog smanjenja.

Abstract (english)

In creating financial, actuarial and medical models, sometimes it's not enough to pay attention only at the time until the end of a particular condition, but it is important to find out the cause of termination. A model that incorporates two random variables, time to termination and cause of termination, is known as multiple decrement model. In this master's thesis, the basic concepts of a double decrement model are defined and explained, and several double decrement models are analyzed. If there is sufficient empirical data quality on the forces of decrement, then a double decrement model can be represented with a double decrement table. In practice, double decrement models are usually given by a double decrement table. The paper presents the construction of double decrement tables through several examples. For each of the causes of decrement in a double decrement model, a single decrement model is defined that depends only on a particular cause of decrement in order to study in detail the impact of one cause of decrement independently of the other cause, and the relationships between the functions of the double decrement model and its associated single decrement model are found.

• Keywords: model višestrukog smanjenja; model dvostrukog smanjenja; model jednostrukog smanjenja
• Keywords (english): multiple decrement model; double decrement model; single decrement model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:664849
• 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: 2020-01-10 11:11:06