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Lecturer(s)
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Course content
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Probability models of the number and amount of claims, their basic characteristics. Distribution models of the number and amount of claims. Extreme losses modeling, Block Maximum Method and Excess Method over High Threshold. Collective risk models - definitions, basic characteristics. Basic types of compound distributions as models of collective risk. Approximation of collective risk model by normal and translated gamma distribution. Monte Carlo collective risk model simulation. Risk premium. Models of individual risk - definition, basic characteristics, approximation and determination of risk premium. Bayesian theory of credibility. Models binomial / beta, Poisson / gamma, normal / normal. Empirical Bayesian models.
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Learning activities and teaching methods
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unspecified, Monologic (reading, lecture, briefing), Methods of individual activities
- Contact teaching
- 52 hours per semester
- Preparation for an exam
- 50 hours per semester
- Home preparation for classes
- 48 hours per semester
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Learning outcomes
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The aim of the course is to apply probabilistic-statistical methods in solving fundamental problems of actuarial science and non-life insurance, such as modeling of number and amount of claims, individual and collective risk models and use of credit theory methods.
The student who has successfully completed the course is able to: correctly assess the real problem in the insurance practice and choose the right computational method for its solution, reasonably and convincingly justify and defend the choice of this method, correctly apply the method using MS Excel or appropriate statistical program package procedures and correctly interpret the results of the application, correctly use the results obtained to reduce actuarial risk.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral examination, Written examination, Student performance assessment
In the academic year 2020/21, in the case of online teaching, FAPS teaching will take place via MS Teams according to the schedule. MS Teams can also be used for consultations. Credit: Credit will be awarded after fulfilling the mandatory attendance at the exercise according to the valid FES UPa directive and after the separate correct solution of all Exercise Tasks, which are at the end of chapters 1-4 of the textbook Applied Insurance Statistics. Exam: written and oral part. The exam in AR 2020/21 will take place in person in the FES UP classroom. The exam has a written part and an oral part. In the written part, the student solves the assigned tasks and answers the so-called small questions. By solving the assigned tasks using MS Excel and Statistica, the student can get 50 points, answers to small questions, the student can get 30 points. The condition for proceeding to the oral part of the exam is at least 50% success in each of the written parts. In the oral part of the exam, the student answers the so-called big question and can get 20 points, when again at least 50% success is required to successfully pass this part of the exam. Small and big questions are available to students in the Stag portal among the published materials on the subject.
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Recommended literature
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BOLAND, J. P. Statistical and Probabilistic Methods in Actuarial Science. Chapman & Hall/CRC, 2007.
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HORÁKOVÁ, G., PÁLEŠ, M., SLANINKA, F. Teória rizika v poistení. Bratislava: Wolters Kluwer, 2015. ISBN 978-80-8168-273-5.
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PACÁKOVÁ, V. a kol. Aplikovaná pojistná statistika. Pardubice: Univerzita Pardubice, 2019. ISBN 978-80-7560-259-6.
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