APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5026 | Stochastic Calculations in Finance | Spring | 3 | 0 | 3 | 8 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Dr. GENCO FAS |
Course Objectives: | This course aims to provide the definition and analysis of stochastic processes arised in financial applications. |
The students who have succeeded in this course; The students who succeeded in this course: ◦will be able to define approximate stochastic process models and analyze them for a given research problem. ◦will be able to provide logical proofs of important theoretical results. ◦will be able to apply the theory of stochastic processes to model real random phenomena. ◦will be able to analyse financial stochastic processes. ◦will be able to model real life financial stochastic processes. |
The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales. |
Week | Subject | Related Preparation | |
1) | Stochastic Processes: Definition and Classification | ||
2) | Risk processes | ||
3) | Poisson and Renewal Processes | ||
4) | Random Walk and Markov Chains (Discrete and Continuous times) | ||
5) | Martigale and Brownian Motion | ||
6) | Black-Scholes Option Pricing Model | ||
7) | Girsanov Theorem for the change of measure arguments | ||
8) | Risk Neutral Pricing and Currency Options with Partial Differential Equations | ||
9) | Pricing and Fixed Income Models | ||
10) | Jump processes and Option Pricing | ||
11) | Dynamic Arbitrage Pricing Theory | ||
12) | Simulation of Dynamic Econometric Models for Asset Returns | ||
13) | Asymptotic Theory for Estimation of Dynamic Econometric Models | ||
14) | Review |
Course Notes: | "Stochastic Processes for Insurance and Finance" by Tomasz Rolski, Hanspeter Schmidli, Volker Schmidt, and Jozef Teugels, John Wiley & Sons, 2009 |
References: | "Stochastic Processes" by Sheldon Ross, Wiley Series in Probability and Mathematical Statistics. "An Introduction to Stochastic Modeling" by S. Karlin and H.E. Taylor. |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 3 | % 15 |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 45 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 1 | 10 | 10 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 3 | 6 | 18 |
Preliminary Jury | 0 | ||
Midterms | 2 | 20 | 40 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 20 | 20 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | |
4) | Ability to make individual and team work on issues related to working and social life. | |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | |
6) | Ability to use mathematical knowledge in technology. | |
7) | To apply mathematical principles to real world problems. | |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |