Course: Actuarial Theory of Risk

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Course title Actuarial Theory of Risk
Course code UMKM/PTRI
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Pacáková Viera, prof. RNDr. Ph.D.
  • Seinerová Kateřina, Ing.
Course content
Subject and importance of the theory of hazard, probability distribution of the number of claims: binomial, Poisson, negative binomial. Distribution of the claim amount, its basic characteristics and use in general insurance in damages modelling. Modelling of the number of claims and claim amount distribution, estimation of parameters distribution, goodness of fit tests. Models of collective hazard - definition, basic characteristics, basic types of compound distribution - compound Poisson, binomial and negative binomial distribution and its basic characteristics. Approximation of the collective hazard model based on normal and translated gamma distribution, calculation of additional netto premium charges. Models of individual hazard - definition, basic characteristics, approximation based on normal distribution and calculation of additional charges. Models of direct insurer damages with the reinsurance of excess of loss and proportional reinsurance - effect of reinsurance for the direct insurer and parameters estimates of censored selection, example of the exponential and Pareto loss distribution. Distribution function and density of claims distribution with the reinsurance of excess of loss and proportional reinsurance, example of exponential and Pareto loss distribution. Bayesian credibility theory, principle of Bayesian estimation theory, prior and posterior distribution, conjugate distribution and Bayesian estimation. Concept of credible premium and factor of credibility, credible Bayesian estimations in the system of insurance, models: binomial/beta, Poisson/gamma, normal/normal. Empirical Bayes estimation of netto premium or total claim amount - models EBCT1 and EBCT2, models prerequisites, parameters estimation.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Skills training, Work-related activities
Learning outcomes
The aim of the course is to apply probability-statistic methods in solving basic insurance problems and general insurance practice, e.g. modelling of the number of claims and claim amount, individual and collective models of hazards, reinsurance, methods of calculation of the credible premium.
Students will be acquainted with theoretical methods as well as with practical skills in applying statistic packages and the table processor Excel.

Assessment methods and criteria
Oral examination, Written examination, Didactic test, Systematic monitoring

The assignment is granted upon completion of the following conditions: attendance at seminars and passing continuous tests. The examination is written and comprises of the theoretical and practical part.
Recommended literature
  • BEARD, R. E. - PENTIKÄINEN, T. - PESONEN,E.:. Risk Theory. London: Chapman and Hall, 1990.
  • BEIRLANT, J., GOEGEBEUR, Y., SEGERS, J., TEUGELS, J.:. Statistics of Extremes: Theory and Aplications. New York: Wiley, 2004.
  • BOLAND, J.P.:. Statistical and Probabilistic Methods in Actuarial Science. Chapman & Hall/CRC, 2007.
  • DICKSON, D. C. M.:. Insurance Risk and Ruin. Cambridge University Press, 2005.
  • EMBRECHTS, P., KLUPPELBERG, C., MIKOSCH, T.:. Modelling extremal events for insurance and finance. Berlin: Springer, 1997.
  • HORÁKOVÁ, G., MUCHA, V.:. Teória rizika v poistení I. Bratislava: Vydavatelství EKONÓM, 2006.
  • KAAS, R., GOOVAERTS, M., DHAENE, J., DENUIT, M.:. Modern actuarial risk theory. Kluwer Academic Publishers, 2001.
  • PACÁKOVÁ, V., a kol. Modelování a simulace pojistných rizik. Pardubice: Univerzita Pardubice: , 2012.
  • Pacáková, V.:. Aplikovaná poistná štatistika. Bratislava: IURA EDITION, 2004.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Economics and Administration Insurance Engineering (2014) Economy 1 Summer
Faculty of Economics and Administration Insurance Engineering (2014) Economy 1 Summer
Faculty of Economics and Administration Insurance Engineering (2013) Economy 1 Summer