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Course info
KMA / PM
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Course description
Department/Unit / Abbreviation
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KMA
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PM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematics for Insurance
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
3
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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To present some models and mathematical methods used in non-life insurance (individual and collective model, compound distribution and its approximations; premium principles, deductibles, credibility theory, bonus-malus systems; reserves, run-off triangles, ruin theory, reinsurance).
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Requirements on student
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FOR WINTER SEMESTER OF SCHOOL YEAR 2017/2018
Knowledge and understanding of the material treated in the course, including the mathematical apparatus used. During the oral exam student gives "exposition" of the chosen topic and answers additional questions of the teacher.
Upon repeated registration of the course, the credit obtained in the previous study of this course is not recognized.
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Content
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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, moment-generating function, conditional distribution. Estimates of parameters. Maximum likelihood method, moment and quantile methods, chi-square goodness-of-fit 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 negative-binomial 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, normal-power, Gram-Charlier approximation. Premium principles. Premiums from long-term perspective, the safety margin. Expected value, standard deviation, variance, quantile, zero-utility, 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 Bühlmann-Straub model. Bonus-malus systems. Bonus classes, Markov chain, limit distribution. Reserves. Reserve for claims and its estimate. Run-off triangles, Chain-Ladder and separation methods. Ruin probability. Insurance claims as a random process, Cramér-Lundberg classical model, differential equations for the probability of ruin in finite and infinite horizon. Estimation of ruin probability. Lundberg adjustment coefficient and Lundberg inequality, Cramer-Lundberg 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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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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26
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Preparation for formative assessments (2-20)
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13
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Preparation for an examination (30-60)
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40
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Total
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79
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
The course assumes knowledge of probability and statistics at least at the introductory course KMA/PSA level (other broader knowledge, or practice with routine use of the apparatus would be an advantage) and uses methods from the introductory courses of mathematical analysis. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
To orientate onself in applications of probability, statistics and random processes in treated areas of non-life insurance, to be able to derive the results presented. In the case of knowledge of the methods of probability and statistics (their detailed exposition is not part of this course) also to apply treated approaches under different conditions. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Textual studies |
Self-study of literature |
Interactive lecture |
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