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Course info
KMA / PRM
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Course description
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Department/Unit / Abbreviation
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KMA
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PRM
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Academic Year
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2016/2017
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Academic Year
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2016/2017
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Title
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Probabilistic Models
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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,
6
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
4
[Hours/Week]
Tutorial
1
[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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Yes in the case of a previous evaluation 4 nebo nic.
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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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Yes in the case of a previous evaluation 4 nebo nic.
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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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1 / -
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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 + Summer
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Semester taught
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Winter + Summer
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Minimum (B + C) students
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not determined
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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 |
every year
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Evaluation scale for credit before examination |
S|N |
| Specification periodicity |
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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 |
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Substituted course
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None
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Preclusive courses
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KMA/PMO
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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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The objective of this course is to study applications of Markov chains. Furthermore, we introduce other random process and probabilistic models. Finally, models and methods from risk theory and decision making are discussed.
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Requirements on student
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Knowledge and understanding of the material and ability to apply it.
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Content
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1. From the theory of probability.
2. Stochastic process.
3. Poisson process.
4. Wiener process.
5. Markov chains with rewards.
6. Controlled chains.
7. Inventory and queuing theory I.
8. Inventory and queuing theory II.
9. Individual and collective model of risk theory.
10. Distribution of the total amount of claims.
11. Calculation and approximation of compound distributions. Premium principles.
12. Credibility theory. Bonus-malus systems. Reinsurance.
13. Reserves. Ruin theory.
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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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-
Recommended:
Sundt, Bjorn. An introduction to non-life insurance mathematics. 4th ed. Karlsruhe : VVW, 1999. ISBN 3-88487-801-8.
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Recommended:
Hušek,R. - Lauber,J. Aplikace stochastických procesů I a II, učební text VŠE. Praha, 1986.
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Recommended:
Mandl, Petr; Mazurová, Lucie. Matematické základy neživotního pojištění. Vyd. 1. Praha : Matfyzpress, 1999. ISBN 80-85863-42-1.
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Recommended:
Bühlmann, Hans. Mathematical methods in risk theory. Berlin : Springer-Verlag, 1996. ISBN 3-540-61703-5.
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Recommended:
Cipra, Tomáš. Pojistná matematika. 1. vydání. Praha : Ekopress, 1999. ISBN 80-86119-17-3.
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Recommended:
Mandl, Petr. Pravděpodobnostní dynamické modely : celost. vysokošk. učebnice pro stud. matematicko-fyz. fakult stud. oboru pravděpodobnost a matem. statistika. Praha : Academia, 1985.
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Recommended:
HUŠEK, R., LAUBER, J. Simulační modely. 1. vyd. Praha : SNTL, 1987.
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Recommended:
Štěpán, Josef. Teorie pravděpodobnosti : Matematické základy : Vysokošk. učebnice pro stud. matematicko-fyz. fakult. Praha : Academia, 1987.
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Recommended:
Prášková, Zuzana; Lachout, Petr. Základy náhodných procesů I.. Vyd. 2., V Matfyzpressu 1. vyd. Praha : Matfyzpress, 2012. ISBN 978-80-7378-210-8.
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On-line library catalogues
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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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Preparation for formative assessments (2-20)
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39
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Presentation preparation (report) (1-10)
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20
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Contact hours
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65
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Preparation for an examination (30-60)
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50
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Total
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174
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| Prerequisites - other information about course preconditions |
| The course assumes knowledge of probability and statistics at least at the introductory course (KMA/PSA) level, other broader knowledge in probability theory, or practice with routine use of the apparatus would be an advantage. The course also makes use of methods of the other introductory mathematics courses (differential and integral calculus, matrices,...). |
| Competences acquired |
| To orientate oneself in treated properties of random processes and their applications, to be able to derive the results presented, to apply them in practical examples and draw practical conclusions. |
| Teaching methods |
- Lecture supplemented with a discussion
- Lecture with practical applications
- Collaborative instruction
- Task-based study method
- Students' self-study
- Self-study of literature
- Lecture
- Practicum
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| Assessment methods |
- Written exam
- Oral exam
- Report
- Skills demonstration during practicum
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