Modelovanie a simulácia rizík v neživotnom poistení

The article focuses on providing brief theoretical definitions of the basic terms and methods of modelling and simulations of insurance risks in non-life insurance by means of mathematical and statistical methods and operational research, and on practical examples of applications of these methods using statistical software.While the risk assessment of insurance company in connection with its solvency is a rather complex and comprehensible problem, its solution starts with statistical modelling of number and amount of individual claims. Successful solution of these fundamental problems enables solving of curtail problems of insurance such as modelling and simulation of collective risk, premium and reinsurance premium calculation, estimation of probability of ruin etc. The article also presents some essential ideas underlying Monte Carlo methods and their appli-cation to modelling of insurance risks. Solving problem is to find the probability distribution of the collective risk in non-life insurance portfolio. Simulation of the compound distribution function of the aggregate claim amount can be carried out, if the distribution functions of the claim number process and the claim size are assumed given. The Monte Carlo simulation is suitable method to confirm the results of other methods and for treatments of catastrophic claims, when small colle-ctives are studied.Analysis of insurance risks using risk theory is important part of the project Solvency II. Risk theory is analysis of stochastic features of non-life insurance processes. The field of application of risk theory has grown rapidly. There is a need to develop the theory into form suitable for practical purposes and to demonstrate their application. Modern computer simulation techniques open up a wide field of practical applications for risk theory concepts, without requiring the restrictive assumptions and sophisticated mathematics. This article presents some comparisons of the tradi-tional actuarial methods and of simulation methods of the collective risk model.