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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ninomiya Syoiti
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr3-4(H137)
- Group
- -
- Course number
- MTH.C504
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 2Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- 2019/7/29
- Language used
- English
- Access Index
-
Course description and aims
In this lecture, the topics discussed in ``Advanced topics in analysis G'' are developed in continuous time models.
The following notions such as Ito integral, Stochastic Differential Equations, and some models in mathematical finance are discussed.
Student learning outcomes
Understanding the following notions:
Ito calculus and basic knowledge of stochastic differential equations
Keywords
Ito calculus, stochastic differential equation, mathematical finance
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Blackboard and handouts
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Ito integral (stochastic integral)(1), definition | Details will be provided each class session. |
| Class 2 | Ito integral (2), basic properties | |
| Class 3 | Ito formula | |
| Class 4 | Ito Representation theorem | |
| Class 5 | Stochastic Differential Equation (1), Existence of the solution | |
| Class 6 | Stochastic Differential Equation (2), Approximations of solutions | |
| Class 7 | Stochastic Differential Equation (3) | |
| Class 8 | Mathematical Finance |
Textbook(s)
None in particular.
Reference books, course materials, etc.
Taniguchi, S., ``Stochastic Differential Equations,'' Kyoritsu
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan
Assessment criteria and methods
Based on reports. Details will be provided in the class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C503 ： Advanced topics in Analysis G
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
Other
None in particular
