Setting the optimal limit value of motor insurance coverage by stochastic optimization

In this paper, we provide an alternative to a passive approach to the selection of insurance products or policy con-ditions. Specifically, we propose a method to make a decision about the optimal limit value for motor insurance coverage. Respecting the stochastic nature of individual loss, we formulate a problem of stochastic programming in which the total potential financial loss of the policyholder is minimized. Actually, we present a general optimization problem in which various relevant probability distributions of individual loss may be considered. In addition, we extend the work of Valecký (2017) and derive an insurance rate that describes better the dependence between the pure premium and the given limit value under the assumption that the individual potential loss follows a gamma distribution. Because of the absence of a closed-form solution, sample average approximation is applied to the objective function and the optimal solution to this approximated (SAA) problem is determined. Finally, the quality of the obtained solution is assessed by approximation to the optimality gap representing the difference between our candidate and the true solution

Note on mismodelling of policyholder's age in claim frequency model: A matter of gender in vehicle insurance

Using the motor hull insurance data of Czech insurer, the paper deals with how mismodelling of policyholder's age can induce misleading conclusions about the gender differences in claim frequency within vehicle insurance. This study is based on individual data with unit policy duration and puts the emphasis on correct modelling of functional form of the age to show that mismodelling as well as categorization yields misleading conclusions and, finally, we demonstrate how the inferences depend on categorization itself. Thus, we showed that linear form as well as the categorization increases the type I error to detect the obvious interaction between gender and age. By involving fractional polynomials, the results partially support the judgement of European Court of Justice to ban using gender as a rating factor, in particular for young policyholders. We concluded that, if another relevant data are not available, the gender as well as interaction with the age should be considered in the claim frequency model although such model cannot be used for setting premium.Web of Science9124022

Analýza a ověření kvality replikace benchmarku metodologií Tracking Error

The aim of the paper is to perform an analysis and compare the accuracy of a benchmark replication using various replication methods of Tracking Error methodology. On the historical data and under the existence of the proportional transactions costs, we verify the impact of stocks number in portfolio and transaction costs on the selected replication methods of passive and active asset management strategies, namely replication with daily and controlled restructuring and the method with penalization of transaction costs. We also determined which selected replication method is the most precise in the sense of benchmark replication and we give several general recommendations for benchmark replication strategy including the eligible proportion of replicating portfolio on the market capitalization with respect to the target replication accuracy. Firstly, the Tracking Error methodology and its application in asset management are presented and optimization problem of particular replication methods is formulated in the next part of the paper. In the application part, the replication accuracy is analyzed and the quality of benchmark replication is verified on the Czech index PX-GLOB during the period of the year 2007. It emerged during our experiment that under the condition of passive asset management strategy the replicating portfolios with the proportion of the market capitalization on the benchmark at the level 70 – 85 % give very good results. Moreover we conclude that the method with penalization of transaction costs is the most precise replication method from the selected and analyzed methods of active assets management strategy

Mikroekonomický scoringový model úpadku českých podniků

The paper is devoted to the proposing a scoring model of firm´s bankruptcy on the basis of logistic regression which could be used in the purpose of classifying the good and bad firms in the Czech Republic. Firstly, the general foundation of logistic regression is described and then the general procedure of model-building strategy including the statistical verification and in-sample validation are explained. Then, we have built the empirical scoring model using results of financial analysis carried out over 400 Czech firms in 2008 and we select such financial ratios with the most substantial prediction capability, i.e. return on assets, current and long-term indebtedness and cash ratio. Our proposed model is fully statistical verified and we also perform the in-sample validation via classification table and ROC curve. Finally, we compare our model with others studies made in this field

An analysis and assessment of financial asset management strategies on the basis of Tracking Error methodology

Prezenční154 - Katedra financívýborn

Aplikace fuzzy-stochastických modelů na tvorbu portfolia finančních aktiv

Prezenční výpůjčkaVŠB - Technická univerzita Ostrava. Ekonomická fakulta. Katedra (154) financ

Self exciting threshold auto-regressive approach for non-linear modeling of daily electricity prices in the selected regions

This paper is focused on the electricity market and electricity prices. The electricity sector is one of the key strategic sectors of every economy and knowledge of demand, supply and prices is very important. Because of the features occurring in the time series of electricity prices (i.e. high frequency, non-constant mean, autocorrelation, non-normal distribution, heteroscedasticity, seasonality, etc.), it is necessary to employ more sophisticated models for the purposes of their modeling. The goal of this paper is to propose the empirical model for modeling daily electricity prices in three selected regions (California, North Europe and Austria). To exploit non-linearity, we apply the SETAR (Self Exciting Threshold Auto-Regressive) models that imply and distinct regimes in time series dynamics with potentially different parameters (and thus dynamics properties) of each regime. First, the most appropriate SETAR model for modeling electricity prices at selected markets is developed; next, statistical verification of each model is performed in accordance with Hansen (1997, 2000); finally, it is verified whether the proposed non-linear models give satisfactory results in the sense of data fitting and diagnostic checks