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Probabilistic modeling of claim sizes, claim counts and aggregate losses. Application of the collective model in
ruin theory and in reinsurance. Introduction to classification ratemaking. Basic methods of claims reserving.
Last update: Branda Martin, doc. RNDr., Ph.D. (13.12.2020)
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The aim of the subject is to describe probabilistic models used in non-life insurance, fundamentals of the collective risk model including elementary ruin theory , to make a survey of technical reserves and selected methods for computing outstanding claims reserves.
Last update: Zichová Jitka, RNDr., Dr. (02.06.2022)
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Requirements to successfully pass the practicals: turn in solutions of homeworks assigned during semestr (in time) and elaborate more extensive project at the end of semester.
The nature of these requirements precludes possibility of additional attempts to obtain the exercise class credit.
The exercise class credit is necessary for the participation in the exam. Last update: Mazurová Lucie, RNDr., Ph.D. (03.10.2024)
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S.A. Klugman, H.H. Panjer, G.E. Willmot: Loss Models: From Data to Decisions. John Wiley & Sons, 1998.
M.V. Wüthrich, M. Merz: Stochastic Claims Reserving Methods in Insurance. Wiley, 2008.
P. Mandl, L. Mazurová: Matematické základy neživotního pojištění. MatfyzPress, 1999. Last update: Branda Martin, doc. RNDr., Ph.D. (13.12.2020)
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Lecture + exercises. Last update: Zichová Jitka, RNDr., Dr. (02.06.2022)
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Oral exam with written preparation. Requirements for the exam consist of the entire extent of the lecture. Last update: Mazurová Lucie, RNDr., Ph.D. (12.10.2022)
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1. Distributions of claim sizes derived by a power transform, generalized and generalized inverse distributional families. Tail behavior, subexponential distributions. 2. (a,b,0) and (a,b,1) classes of counting distributions. 3. Panjer recursive formula for compound distributions. Methods of discretization of a continuous claim size distribution. Calculation of a compound distribution by means of FFT. Approximations of the aggregate loss distribution. 4. Discrete-time ruin theory model. 5. Pricing of XL-reinsurance with reinstatements. 6. Simple methods of classification ratemaking. Loglinear model. 7. Mack's model and chain-ladder method. Bornhuetter-Ferguson method. Poisson model for incremental development triangles.
Last update: Mazurová Lucie, RNDr., Ph.D. (13.12.2020)
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Basics of probability theory: probabilty distribution, conditioning, moment generating function, moments, conditional expected value Last update: Mazurová Lucie, RNDr., Ph.D. (21.04.2024)
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