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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Fukaya Ryuji
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Wed9-10(H137)
- Group
- -
- Course number
- MTH.D401
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 1Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course and the subsequent Advanced Topics in Mathematical Finance B will explain global investment strategies making use of mathematical finance. Discussions will especially focus on the differences in investment strategies depending on the various characteristics of funds for investment, investment objectives, and the investor's tolerance of risk.
Student learning outcomes
By the end of this course and the subsequent "Advanced Topics in Mathematical Finance B", students will know how to build a stochastic process model of asset returns using probabilistic analysis and solve the problem of maximizing expected utility using the discrete time model and the continuous time model.
Keywords
International investment strategies, optimal portfolio strategies, Asset-Liability Managements, maximization of expected utilities, stochastic differential equations, stochastic flows, Malliavin Calculus.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This course consists of learning using blackboards, projectors, and distributed materials.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Risks, returns, and asset allocation strategies | Details will be provided during each class session. |
| Class 2 | Foreign exchange rates | |
| Class 3 | Fixed income investments (1) | |
| Class 4 | Fixed income investments (2) | |
| Class 5 | Asset Pricing Theory (1) | |
| Class 6 | Asset Pricing Theory (2) | |
| Class 7 | Applications of Asset Pricing Theory; term structures of interest rates | |
| Class 8 | Applications of Asset Pricing Theory; multi-currency world |
Textbook(s)
None in particular
Reference books, course materials, etc.
None in particular
Assessment criteria and methods
Based on reports. Details will be provided in class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C507 ： Advanced topics in Analysis G1
- MTH.C508 ： Advanced topics in Analysis H1
- MTH.D402 ： Advanced Topics in Mathematical Finance B
- MTH.D403 ： Advanced Topics in Mathematical Finance C
- MTH.D404 ： Advanced Topics in Mathematical Finance D
- MTH.E440 ： Special lectures on advanced topics in Mathematics Q
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
