2020 Advanced Topics in Mathematical Finance B

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Fukaya Ryuji 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Wed9-10(H137)  
Group
-
Course number
MTH.D402
Credits
1
Academic year
2020
Offered quarter
2Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course, following Advanced Topics in Mathematical Finance A, will explain global investment strategies making use of mathematical finance.

Student learning outcomes

By the end of this course, students will know how to build a stochastic process model of asset returns using probabilistic analysis and solve the problem of maximizing expected utility using the discrete time model and the continuous time model.

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 research director.

Keywords

International investment strategies, optimal portfolio strategies, Asset-Liability Managements, maximization of expected utilities, stochastic differential equations, stochastic flows, Malliavin Calculus.

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

This course consists of learning using blackboards and distributed materials.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Optimal portfolio strategies: continuous-time models (1) Details will be provided in each class session.
Class 2 Optimal portfolio strategies: continuous-time models (2)
Class 3 Stochastic differential equations and stochastic flows (1)
Class 4 Stochastic differential equations and stochastic flows (2)
Class 5 Malliavin Calculus (1)
Class 6 Malliavin Calculus (2)
Class 7 Optimal portfolio strategies: continuous-time models (3)

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.

None in particular

Assessment criteria and methods

Based on reports. Details will be provided in class.

Related courses

  • MTH.C361 : Probability Theory
  • MTH.C507 : Advanced topics in Analysis G1
  • MTH.C508 : Advanced topics in Analysis H1
  • MTH.D401 : Advanced Topics in Mathematical Finance A
  • MTH.D403 : Advanced Topics in Mathematical Finance C
  • MTH.D404 : Advanced Topics in Mathematical Finance D
  • MTH.E440 : Special lectures on advanced topics in Mathematics Q

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular

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