|
|
Quantifying Mortality and Longevity Risk by Means of Stochastic Models
Plotnikova, Valeriya ; Mazurová, Lucie (advisor) ; Kříž, Pavel (referee)
In this thesis we investigate the structure of the generalized age-period-cohort mortality model and we comment on the key components of its structure. As an example of the generalized age- period-cohort model we take a closer look at the widely used Lee-Carter mortality model. We further construct mortality models for the Czech male and female populations, by using a certain procedure that involves expert judgment. To project mortality rates we choose the most suitable time series processes for the selected parameters in the model. Finally, we describe and implement the value at risk framework for the longevity risk, which is one of the possible applications where the obtained mortality models can be used in practice. In particular, we investigate how much a temporary life annuity liability might change based on new information over the course of one year.
|
|
|
Stochastic mortality models within the quantification of selected actuarial risks
Šešulka, Marek ; Hendrych, Radek (advisor) ; Mazurová, Lucie (referee)
The thesis focuses on the stochastic mortality models in the context of actuarial risks. In the theoretical part, the thesis defines five mortality models with approaches to prediction. After that, it follows the description of selected actuarial risks in the context of mortality. Hedging of longevity risk is obtained through a financial instrument called a longevity bond. Pricing of that bond is delivered via the Wang transformation approach. In the empirical part of the thesis, there are carried out estimates, interpretations, and comments for models based on the Czech mortality data. Later, prediction tests are executed for an individual model, both sex and two chosen ages. The last part of the empiric section deals with the data driven pricing of longevity bond and the price of risk.
|
|
|
Modelling mortality differentials by age
Šuléřová, Natálie ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This diploma thesis deals with sex-specific mortality modelling, that is modelling in two populations - female and male, with emphasis on models considering the inter- dependence between these populations. Four models were theoretically described in the thesis - independent Lee-Carter model, the common factor model, the augmented com- mon factor model and the credibility model. All models were then applied to real mortality data in the female and male population of the Czech Republic and compared with each other. Mortality rates for Czech females and males were predicted by selected models. Finally, the effect of including a common factor in mortality modelling was analyzed in comparison with independent modelling in both populations as the difference in a lia- bility value arising from selected life insurance products. 1
|
|
| |
|
|
Solvency II Methods for Life Insurance
Benešová, Martina ; Finfrle, Pavel (advisor) ; Mazurová, Lucie (referee)
Název práce: Metodiky Solvency II v životním pojištění Autor: Martina Benešová Katedra (ústav): Katedra pravděpodobnosti a matematické statistiky Vedoucí bakalářské práce: RNDr. Pavel Finfrle, Ph.D e-mail vedoucího: finfrle@generalippf.eu Abstrakt: Tato diplomová práce se zabývá problematikou solventnosti pojišťoven v souvislosti s konceptem regulatorního rámce Solvency II. Na začátku práce jsou shrnuté základní body o Solvency I, dále je větší pozornost věnovaná vlastnostem Solvency II a jednotlivým kategoriím rizik, jejichž správná kvantifikace je pro Solvency II klíčová. V další části jsou představeny metody na výpočet kapitálové dostatečnosti - interní a částečné interní modely a podrobněji pak standardní model. Klíčové dvě kapitoly práce se pak detailně zabývají rizikem storen v ži- votním pojištění. Rozebrána je standardní metodika výpočtu kapitálového poža- davku, a je navržen stochastický model, který ji rozšiřuje zahrnutím informace o diverzitě odbytových cest. Monte Carlo simulací je demonstrována nižší rizikovost pojišťovny s širším polem zprostředkovatelů. Klíčová slova: solventnost, Solvency II, kapitálové požadavky, riziko storen Title: The methods of Solvency II for life insurance Author: Martina Benešová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Pavel...
|
|
|
Lapse Analysis of Insurance Contracts
Strnad, Jan ; Mertl, Jakub (advisor) ; Mazurová, Lucie (referee)
The aim of the present work is to develop a tool for identification of Motor Third Party Liability insurance contracts which are at risk of cancellation. Methods for explorative data analysis, building a logistic regression model, comparing models and their validation and calibration are presented. Several models are developed on the real dataset using mentioned methods and then the final one is chosen. Behavior of the final model is verified by the validation on the out-of-time sample. Last step is calibration of the model to the expected value of the future portfolio cancellation rate.
|
|
| |
|
|
Statistical models for capital models of insurance companies
Švagerková, Lýdia ; Šimurda, Miroslav (advisor) ; Mazurová, Lucie (referee)
This work deals with the topic of lapse rate modelling in the field of Life Insurance. First, the theoretical apparatus is established: the linear models and their extension, generalized linear models. Furthermore, we describe the process of model selection and evaluation. In the second part of this work we describe the influence of various individual as well as macroeconomical parameters on the lapse rate. We summarize the findings of previous works in this field. The last part introduces models in statistical software R based on generalized linear models and describes the process of their selection and evaluation. Outputs from these models are interpreted and compared to the ratio analysis results.
|
|
|
Identification and accounting the changes in calculation of the IBNR reserves.
Brdíčková, Jana ; Trchová, Radka (advisor) ; Mazurová, Lucie (referee)
This text describes wide variety of models for IBNR reserve estimation, among them we can find chain ladder, Munich chain ladder, Cape Cod or regression methods. Especially, it aims at identification of model assumptions, its verification, impacts of their non-fulfillment and resulting model modification. Moreover, this work deals with anomalies and specificity of historical data and tries to suggest solutions for this problems. The last part of the thesis is dedicated to real analysis of motor third party liability.
|
|
|
Claims reserve calculation for data separating true IBNR and IBNER
Šťástka, Petr ; Mazurová, Lucie (advisor) ; Justová, Iva (referee)
The thesis deals with calculating technical reserves of non-life insurance undertakings, especially calculating the claims reserve, which is the most important non-life insurance reserve. It describes the reserve for claims in detail focusing consequently on the different calculation methods. The thesis focuses particularly on the description of the model proposed by the Swiss mathematician René Schnieper. This is a special model aimed at estimating the ultimate claims based on the decomposition of the incurred data into new claims amounts and changes in incurred amounts for the existing claims reported in the earlier years of the development. The final chapter numerically illustrates and compares the methods mentioned in this thesis.
|
guest ::
