FOR WINTER TERM OF SCHOOL YEAR 2017/2018 Introduction. Some statistical indicators in insurance. Individual and collective model. Distribution of the amount of insurance claims. Exponential, gamma, log normal, Weibull, and Pareto distributions, skewness, momentgenerating function, conditional distribution. Estimates of parameters. Maximum likelihood method, moment and quantile methods, chisquare goodnessoffit test. Example. Distribution of the number of insurance claims. Poisson, negative binomial, and mixed Poisson distributions. Generating functions of probability distribution, example. Distribution of the total amount of claims. Compound distribution and its characteristics. Compound Poisson distribution, sums of compound Poisson distributions. Compound negativebinomial distribution, the interpretation as a compound Poisson. Approximation of individual model by collective model. Deductibles and reinsurance. Proportional and fixed amount deductibles, distribution of the number and amount of claims paid by insurer. Proportional, XL, and SL reinsurance. Distribution of claims paid by cedant, estimates of parameters. Calculation and approximation of compound distributions. Panjer recurrent formula, moments. Approximations by shifted distribution, Edgeworth, normalpower, GramCharlier approximation. Premium principles. Premiums from longterm perspective, the safety margin. Expected value, standard deviation, variance, quantile, zeroutility, exponential priciples and their properties. Credibility theory. Homogeneous and inhomogeneous collective of risks, collective and individual premiums. American credibility theory, full and partial credibility. Bayesian credibility theory, Bayesian and linear credibility premiums. Bühlmann and BühlmannStraub model. Bonusmalus systems. Bonus classes, Markov chain, limit distribution. Reserves. Reserve for claims and its estimate. Runoff triangles, ChainLadder and separation methods. Ruin probability. Insurance claims as a random process, CramérLundberg classical model, differential equations for the probability of ruin in finite and infinite horizon. Estimation of ruin probability. Lundberg adjustment coefficient and Lundberg inequality, CramerLundberg approximation, approximation of adjustment coefficient. Influence of reinsurance to adjustment coefficient, proportional reinsurance. Additional information on the web page http://home.zcu.cz/~friesl/Vyuka/Pm.html


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