2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced Topics in Mathematical Finance A
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ryuji Fukaya
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 9-10 Wed
- Class
- -
- Course Code
- MTH.D401
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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.
Course description and aims
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.
Student learning outcomes
実務経験と講義内容との関連 (又は実践的教育内容)
The lecturer has been working in a financial institute as a research director.
Keywords
International investment strategies, optimal portfolio strategies, Asset-Liability Managements, maximization of expected utilities, stochastic differential equations, stochastic flows, Malliavin Calculus.
Competencies
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None in particular
Reference books, course materials, etc.
Shigeo Kusuoka, Stochastic Analysis, (Monographs in Mathematical Economics, 3), Springer
Evaluation methods and criteria
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
None in particular
Other
None in particular