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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shinozaki Yuji Nakayama Toshiyuki Ninomiya Syoiti
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (本館2階201数学系セミナー室)
- Group
- -
- Course number
- MTH.E440
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/8/30
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
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
Student learning outcomes
・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
Course taught by instructors with work experience
| ✔ Applicable | How instructors' work experience benefits the course |
|---|---|
|
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 that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
Textbook(s)
Details will be provided during each class session
Reference books, course materials, etc.
Details will be provided during each class session
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.C361 ： Probability Theory
- MTH.C507 ： Advanced topics in Analysis G1
- MTH.C508 ： Advanced topics in Analysis H1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
