2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Special lectures on advanced topics in Mathematics Q
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yuji Shinozaki / Toshiyuki Nakayama / Syoiti Ninomiya
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- MTH.E440
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
In this course, theoretical backgrounds and applications on mathematical finance will be described. The main aims of this course are to introduce some practical aspects of the mathematical finance and to present the mathematical formulations of practically important financial problems.
For example, the following topics would be introduced with some assignments of computer programmings
1. Overview of financial mathematics
2. Foundation of mathematical finance
3. Problems of interest rate modeling and introduction to stochastic analysis in infinite dimension
4. Application of stochastic partial differential equations to mathematical finance
5. Numerical analysis of stochastic differential equations
Course description and aims
・Understand how the probability theory and the mathematical finance are used in the financial institution
・Be able to survey the recent hot topics of mathematical finance
・Get conscious about linkages of pure mathematics to the real world
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 quants.
Base on my professional experience as a derivative quant in the financial industry, I'll give some examples that theory of Mathematical finance is effective in practice.
Keywords
Quant, Mathematical finance, Derivative quant, Arbitrage free pricing theory, Stochastic (partial) Differential Equation, Monte Carlo simulation
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course with the presentation slides and black boards. There will be some assignments.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Overview of financial mathematics | Details will be provided during each class |
| Class 2 | Foundation of mathematical finance | Details will be provided during each class |
| Class 3 | Problems of interest rate modeling and introduction to stochastic analysis in infinite dimension | Details will be provided during each class |
| Class 4 | Application of stochastic partial differential equations to mathematical finance | Details will be provided during each class |
| Class 5 | Numerical analysis of stochastic differential equations | Details will be provided during each class |
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)
Details will be provided during each class session
Reference books, course materials, etc.
Details will be provided during each class session
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.C361 ： Probability Theory
- MTH.C507 ： Advanced topics in Analysis G1
- MTH.C508 ： Advanced topics in Analysis H1
Prerequisites
None in particular