na študijskem programu 2. stopnje Matematika
Polona Kren (Author), Marko Jakovac (Mentor)

Abstract

V magistrskem delu so predstavljeni modeli več stanj za življenjska zavarovanja. Delo je razdeljeno na dva dela, na teoretični in praktični del. V teoretičnem delu so najprej predstavljene osnovne definicije iz verjetnosti in statistike. Nato je opisana osnovna aktuarska notacija in definirana jakost smrtnosti. Sledi predstavitev osnovnih modelov več stanj in predpostavk, vezanih nanje. Prikazana je izpeljava formul za verjetnosti prehoda ob znanih jakostih prehodov. Opisan je tudi izračun aktuarskih sedanjih vrednosti, izračun premije in vrednotenje polic takšnih modelov. Na koncu je še predstavljen način oblikovanja rezervacij življenjskih polic. V praktičnem delu je prikazano, kako lahko ob znanih jakostih prehoda zgradimo zavarovanje za dolgotrajno oskrbo. V programu Python pa je izračunana tudi neto premija za takšno zavarovanje (koda je podana v prilogi).

Keywords

magistrska dela;življenjsko zavarovanje;zavarovalstvo;stohastični procesi;Markovske verige;premija;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [P. Kren]
UDC: 519.21(043.2)
COBISS: 200985347 Link will open in a new window
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Downloads: 6
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Other data

Secondary language: English
Secondary title: Multiple state models for life insurance
Secondary abstract: In this master's thesis, multiple-state model for life insurance is presented. The work is divided into two parts, a theoretical section, and an experimental section. In the theoretical section, fundamental definitions from probability and statistics are initially introduced. Then, the basic actuarial notation and the concept of force of mortality are described. This is followed by the introduction of basic multiple-state models and the assumptions associated with them. The derivation of formulas for transition probabilities, given known transition intensities, is demonstrated. Additionally, the calculation of actuarial present values, premium, and policy evaluation for these models are explained. Finally, the method for establishing reserves for life insurance policies is presented. In the practical section, the construction of long-term care insurance based on known transition intensities is demonstrated. The net premium for such insurance is calculated using Python, with the code provided in the appendix.
Secondary keywords: master theses;life insurance;insurance;stochastic processes;Markov chains;premium;Življenjsko zavarovanje;Markovski procesi;Univerzitetna in visokošolska dela;
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VIII, 65 f.
ID: 24248418