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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.)
- Tue5-6(H119A)
- Group
- -
- Course number
- MTH.C507
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 3Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This lecture and its sequel ``Advanced topics in analysis H1'' are aimed at those wishing to learn about the basic mathematical concepts of mathematical finance. The following notions, continuous time martingales, Brownian motion, stochastic integral, stochastic differential equations, and the Black-Scholes model are discussed in these two lectures. In this lecture we start from the introduction of stochastic processes, develop the theory of martingales, and introduce the definition of the Brownian motion.
Student learning outcomes
Students are expected that they understand the basic notions of continuous time martingales and Brownian motion.
Keywords
Mathematical Finance, Martingale(discrete time)
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 | Probability theory | Details will be provided during each class session |
| Class 2 | stochastic processes | |
| Class 3 | discrete time martingale | |
| Class 4 | Doob's inequality/Stopping time/Optional Sampling theorem | |
| Class 5 | Martingale | |
| Class 6 | Quadratic Variation | |
| Class 7 | Brownian Motion(1) | |
| Class 8 | Browninan Motion(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.C361 ： Probability Theory
- MTH.C508 ： Advanced topics in Analysis H1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
syoiti.ninomiya+AG[at]gmail.com
Other
None in particular
