|
|
Main menu for Browse IS/STAG
Course info
KMA / PRM
:
Course description
Department/Unit / Abbreviation
|
KMA
/
PRM
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Probabilistic Models
|
Form of course completion
|
Exam
|
Form of course completion
|
Exam
|
Accredited / Credits
|
Yes,
6
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Lecture
4
[Hours/Week]
Tutorial
1
[Hours/Week]
|
Course credit prior to examination
|
Yes
|
Course credit prior to examination
|
Yes
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
YES
|
Language of instruction
|
Czech
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
0 / -
|
0 / -
|
0 / -
|
Included in study average
|
YES
|
Winter semester
|
0 / -
|
0 / -
|
0 / -
|
Repeated registration
|
NO
|
Repeated registration
|
NO
|
Timetable
|
Yes
|
Semester taught
|
Winter semester
|
Semester taught
|
Winter semester
|
Minimum (B + C) students
|
not determined
|
Optional course |
Yes
|
Optional course
|
Yes
|
Language of instruction
|
Czech
|
Internship duration
|
0
|
No. of hours of on-premise lessons |
|
Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
|
Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
|
None
|
Preclusive courses
|
KMA/PMO
|
Prerequisite courses
|
N/A
|
Informally recommended courses
|
N/A
|
Courses depending on this Course
|
N/A
|
Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
|
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.
|
Requirements on student
|
Knowledge and understanding of the material and ability to apply it.
Upon repeated registration of the course, the credit obtained in the previous study of this course is not recognized.
|
Content
|
1. From the theory of probability.
2. Stochastic process.
3. Poisson process.
4. Wiener process.
5. Markov chains with rewards.
6. Controlled chains.
7. Renewal theory.
8. Inventory and queuing theory.
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.
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
-
Recommended:
Sundt, Bjorn. An introduction to non-life insurance mathematics. 4th ed. Karlsruhe : VVW, 1999. ISBN 3-88487-801-8.
-
Recommended:
Hušek,R. - Lauber,J. Aplikace stochastických procesů I a II, učební text VŠE. Praha, 1986.
-
Recommended:
Mandl, Petr; Mazurová, Lucie. Matematické základy neživotního pojištění. Vyd. 1. Praha : Matfyzpress, 1999. ISBN 80-85863-42-1.
-
Recommended:
Bühlmann, Hans. Mathematical methods in risk theory. Berlin : Springer-Verlag, 1996. ISBN 3-540-61703-5.
-
Recommended:
Cipra, Tomáš. Pojistná matematika. 1. vydání. Praha : Ekopress, 1999. ISBN 80-86119-17-3.
-
Recommended:
Mandl, Petr. Pravděpodobnostní dynamické modely : celost. vysokošk. učebnice pro stud. matematicko-fyz. fakult stud. oboru pravděpodobnost a matem. statistika. Praha : Academia, 1985.
-
Recommended:
HUŠEK, R., LAUBER, J. Simulační modely. 1. vyd. Praha : SNTL, 1987.
-
Recommended:
Štěpán, Josef. Teorie pravděpodobnosti : Matematické základy : Vysokošk. učebnice pro stud. matematicko-fyz. fakult. Praha : Academia, 1987.
-
Recommended:
Prášková, Zuzana; Lachout, Petr. Základy náhodných procesů I.. Vyd. 2., V Matfyzpressu 1. vyd. Praha : Matfyzpress, 2012. ISBN 978-80-7378-210-8.
-
On-line library catalogues
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Preparation for formative assessments (2-20)
|
39
|
Presentation preparation (report) (1-10)
|
20
|
Contact hours
|
65
|
Preparation for an examination (30-60)
|
50
|
Total
|
174
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
formulovat a vysvětlit základní pojmy pravděpodobnosti a statistiky (v rozsahu předmětu KMA/PSA), podrobnější znalosti z teorie pravděpodobnosti či jejich aparátu jsou výhodou |
popsat a vysvětlit základní pojmy diferenciálního a integrálního počtu (v rozsahu předmětů KMA/M1 a KMA/M2) |
popsat a vysvětlit základní pojmy maticového počtu (v rozsahu předmětu KMA/LA) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat diferenciální počet na praktické úlohy |
odlišit různé typy náhodných veličin (diskrétní, spojité) a různé typy rozdělení |
používat základní operace maticového počtu |
vypočítat určité i neurčité integrály (známých typů) v jedné dimenzi metodou per-partes nebo substituční metodou |
využívat znalostí základních statistických metod a postupů pro jednoduchou analýzu dat |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
orientovat se v probraných vlastnostech náhodných procesů a jejich aplikacích |
Skills - skills resulting from the course: |
odvodit vyložené výsledky a vlastnosti náhodných procesů a jejich aplikací |
uplatnit teoretické výsledky v praktických příkladech a vyvodit praktické závěry |
Competences - competences resulting from the course: |
N/A |
N/A |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Oral exam |
Skills demonstration during practicum |
Written exam |
Skills - skills achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Oral exam |
Skills demonstration during practicum |
Written exam |
Competences - competence achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Oral exam |
Skills demonstration during practicum |
Written exam |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Collaborative instruction |
Interactive lecture |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Self-study of literature |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Collaborative instruction |
Interactive lecture |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Self-study of literature |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Collaborative instruction |
Interactive lecture |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Self-study of literature |
|
|
|
|