| Course title | Probability Decision and Stochastic Models in Economy |
|---|---|
| Course code | KMI/KPRSM |
| Organizational form of instruction | Lecture |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory-optional |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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Lectures: 1 - Introduction to the course. Probability - basic terminology, stochastic event, random variable, conditional probability, probability trees. 2 - Bayesian formula. Sampling and perfect information. Bayesian approach to decision making. 3 - Decision making and risk , utility function under risk. 4 - Game theory - basic terminology, dominated and non-dominated strategy. 5 - Two players game, antagonistic and non-antagonistic problems. Nash equilibrium. 6 - Cooperative and non-cooperative games, pure and mixed strategies. 7 - Graphic solution of games, the solution using linear programming. 8, 9 - Markov chains (transition probabilities, limit probabilities, ergodic and stationary chains). 10, 11 - Inventory models (basic terminology, deterministic models, some of the stochastic models). 12 - Queuing models (introduction, characteristic of queuing models - calling population, customer arrivals, the waiting line, processing order; basic single-channel model.). 13 - Renewal models (renewal models of obsolete and malfunction units). Seminars: 1 - Revision of basic terminology of probability. 2 - Probability trees. 3 - Bayesian formula. Sampling and perfect information. 4 - Decision making and risk , utility function under risk. 5 - 8 - Game theory. 9, 10 - Markov analysis. 11,12 - Inventory models. 13 - Queuing models.
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| Learning activities and teaching methods |
| Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration |
| Learning outcomes |
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The aim of the course is to develop students' probabilistic thinking, to introduce them decision making under risk and to demonstrate the principles of the solving of risk problems. The course uses the knowledge from courses Statistics I and Operational analysis to introduce the stochastic models in economy.
Students understand the basic principles of probability, they will better decide in situations with random results. |
| Prerequisites |
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Basic knowledge of the course Mathematics I, Statistics I and Operation analysis.
KMI/COV ----- or ----- KMI/KOA ----- or ----- KMI/OA ----- or ----- KMI/OAA ----- or ----- KMI/OV ----- or ----- KMI/OVA and KMI/KTPS ----- or ----- KMI/KTPSA ----- or ----- KMI/TPS ----- or ----- KMI/TPSA ----- or ----- KMI/YTPS and KMI/KTPSA |
| Assessment methods and criteria |
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Combined exam, Test
Credit Requirements: At least 18 points out of 30 in three credit tests (each of them is worth a maximum of 10 points, the first two are based on the seminar works). Examination Requirements: An exam consists from written and oral parts. The written part of the exam contains simple problems - to solve them students must prove knowledge of the themes, ability to apply explained methods and usage of appropriate software. The oral part involves discussion about seminar works, analysis of the written exam part and supplemental questions from other themes. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Economics | Study plan (Version): Financial and Insurance Mathematics (4) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |