2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced Topics in Mathematical Finance B
- 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.D402
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course, following Advanced Topics in Mathematical Finance A, will explain global investment strategies making use of mathematical finance.
Course description and aims
By the end of this course, 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 and distributed materials.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Optimal portfolio strategies: continuous-time models (1) | Details will be provided in each class session. |
| Class 2 | Optimal portfolio strategies: continuous-time models (2) | |
| Class 3 | Stochastic differential equations and stochastic flows (1) | |
| Class 4 | Stochastic differential equations and stochastic flows (2) | |
| Class 5 | Malliavin Calculus (1) | |
| Class 6 | Malliavin Calculus (2) | |
| Class 7 | Optimal portfolio strategies: continuous-time models (3) |
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.
Hiroyuki Matsumoto, Setuo Taniguchi, Stochastic Analysis:Ito and Malliavin Calculus in Tandem (Cambridge Studies in Advanced Mathematics Book 159) , Cambridge University Press
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.D401 ： Advanced Topics in Mathematical Finance A
- 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