Michal Páleš, Faculty of Economic Informatics, University of Economics in Bratislava, Slovak Republic

Pages: 3 – 17

Abstract

One of the tasks of risk analysis is to determine the most appropriate stochastic model using a random variable describing the data available. These models are the basic units of the more sophisticated models intended for risk quantification. In the collective risk model, the probability distribution of the number of claims, individual claim amount and the aggregate claim distribution is thereafter predicted. Consequently, it is important to choose the risk measures by which the examined risk will be measured. One of the useful risk measurement methods is the value at risk (VaR) method for the determination of quantiles of the respective distributions and which may be extended by a coherent conditional value at risk (CVaR). On the basis of these values, the business capital assuring the insurance company solvency with high probability can be modelled by an actuary. The VaR risk measures and in particular the CVaR can be determined by a number of methods, most of which are not simple. This paper introduces the simulation tools of the R language, enabling the actuary the sophisticated estimation of values.