2021 Advanced topics in Analysis H

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Ninomiya Syoiti 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Thr3-4()  
Group
-
Course number
MTH.C504
Credits
1
Academic year
2021
Offered quarter
2Q
Syllabus updated
2021/4/15
Lecture notes updated
-
Language used
English
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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

Out-of-Class Study Time (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)

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

Information about this lecture will be announced via T2SCHOLA.

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