▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Analysis H1
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- 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.)
- Tue5-6(H119A)
- Group
- -
- Course number
- MTH.C508
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 4Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- 2019/1/29
- Language used
- Japanese
- Access Index
-
Course description and aims
In this lecture, the theory of Ito integral (stochastic integral) is introduced. We start from the definition of the Ito integral and the Ito formula is introduced. Then we develop some important aspects of stochastic differential equations. As an application of Girsanov's theory and martingale representation, the Black-Scholes formula is derived.
Student learning outcomes
Students are expected that they understand the notion of stochastic integral, are able to use the Ito formula properly, and understand the relations between the basic notion of the theory of mathmatical finance and stochastic integrals.
Keywords
Stochastic Integral, Ito formula, 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 | Stochastic Integral/Ito formula | Details will be provided during each class session |
| Class 2 | Representation theorem | |
| Class 3 | Stochastic Differential Equation/Solution | |
| Class 4 | Properties of solutions to stochastic differential equations/Storong markov property | |
| Class 5 | Stochastic Differential Equation(2)/Exponential martingale/Girsanov's theorem | |
| Class 6 | Feynmann-Kac formula/Heat Equation | |
| Class 7 | Application to mathematical finance(1) | |
| Class 8 | Application to mathematical finance(2) |
Textbook(s)
None in particular
Reference books, course materials, etc.
D. Williams, ``Probability with Martingales'', Cambridge
R. J. Elliott and P. E. Kopp, ``Mathematics of Financial Markets'', Springer
N. Ikeda, S. Watanabe, "Stochastic Differential Equations and Diffusion Processes", North Holland
Assessment criteria and methods
Based on reports
Related courses
- MTH.C507 ： Advanced topics in Analysis G1
- MTH.C361 ： Probability Theory
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Knowledge about basic continuous time stochastic processes (Advanced topics in Analysis G1)
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
syoiti.ninomiya+AH[at]gmail.com
Other
None in particular
