|
|
Modelling dependent lives
Pavčová, Eva ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Title: Modelling Dependent Lives Author: Eva Pavčová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we model the dependence between the remaining lifetimes of a husband and wife using a specific Markov model. We examined the impact of the dependence on the net single premium using the specific Markov model that captures the long-term dependence between lifetimes of the two considered lives. Using this model we have calculated 10-year joint-life annuity due and 10-year last-survivor annuity due considering the age rage (37, 80) in case of dependence and also independence of the two considered lives. The calculations were based on the dataset related to the Czech population in 2015. The impact of the dependence between the remaining lifetimes of the husband and wife was found to be not significant. Keywords: positive quadrant depedence, multiple life insurance premiums, depen- dent lifetimes, joint-life annuity, last-survivor annuity, joint-life and last-survivor models
|
|
|
Selected problems of random walks
Pavčová, Eva ; Hlubinka, Daniel (advisor) ; Pawlas, Zbyněk (referee)
Title: Selected problems of random walks Author: Eva Pavčová Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D., Department of Probability and Mathematical Statistics Abstract: This thesis deals with simple random walks and solutions of theoretical selected problems. We define the path which can be interpreted as the realization of a random walk. We bring forward examples of paths with illustrations and basic properties such as ballot theorem and reflection principle. Random walk is defined and also the probability of its is brought forward. Our attention is concentrated on the main lemma. We derive from it other interesting assertions such as arcsin law. The aim of this thesis is to solve the selected problems using theoretical knowledge. The problems are concerned with probabilities and numbers of paths with certain restrictions. The specific problem of positive paths proves geometrically the equality of numbers of two types of paths. Specially, we are interested in the proof of reformulation of main lemma. Keywords: path, reflection principle, main lemma, arcsin law
|
guest ::
