2021 Advanced Topics in Mathematical Finance A

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Academic unit or major
Graduate major in Mathematics
Fukaya Ryuji 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course and the subsequent Advanced Topics in Mathematical Finance B will explain global investment strategies making use of mathematical finance. Discussions will especially focus on the differences in investment strategies depending on the various characteristics of funds for investment, investment objectives, and the investor's tolerance of risk.

Student learning outcomes

By the end of this course and the subsequent "Advanced Topics in Mathematical Finance B", 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.


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, projectors, and distributed materials.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Risks, returns, and asset allocation strategies Details will be provided during each class session.
Class 2 Foreign exchange rates
Class 3 Fixed income investments (1)
Class 4 Fixed income investments (2)
Class 5 Asset Pricing Theory (1)
Class 6 Asset Pricing Theory (2)
Class 7 Applications of Asset Pricing Theory

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.


None in particular

Reference books, course materials, etc.

Shigeo Kusuoka, Stochastic Analysis, (Monographs in Mathematical Economics, 3), Springer

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.D402 : Advanced Topics in Mathematical Finance B
  • 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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