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Profitability of life policies and compound GLM
Kostka, Ján ; Pešta, Michal (advisor) ; Komárek, Arnošt (referee)
Life insurance policies are not equally profitable is sense of expected value. In practice, profitability is an output of complex cash flow models, which need utilizing special systems and the run time of such calculation can be significant if number of policies is high. Therefore we consider variables, which change most frequently, stimulate the profitability model with several values of these variables and then we search for a regression model to explain the changes. We apply Gamma regression on the data. But what if there exist some policies which are negative? Then we determine these policies with logistic regression applied on data censored to the binary form. Loss of these policies is modelled using symmetrical Gamma model. These three models, when considered together, can be viewed as a single model, which is a generalization of the well known zero inflated count model. The most interesting part of inference in such model is diagnostics. We show that the basic types of residuals - Pearson, deviance and quantile - can be defined. We also build an ordinary linear model and we compare utility of these two approaches. While building models, we meet various statistical issues like dimension reduction of yield curve or dispersion proportional to sum insured. 1
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Linear regression model with autocorrelated residuals
Kostka, Ján ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
The aim of this bachelor thesis is to introduce the algorithm for analysis of the linear regression model with autocorrelated residuals, which is applicable to time series data. For residuals, we assume the ARMA model, eventually ARIMA model, which enlarges the possibilities of application. The analysis of such regression models includes detection of autocorrelation and related tests, detection of stationarity and related unit root test, followed by model identification for residuals and maximum likelihood estimation of identified regression model.
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