2021 Special lectures on advanced topics in Mathematics Q

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

In this course, some topics on mathematical finance will be described with practical examples. The main aims of this course are to introduce some practical aspects of the mathematical finance and to present the mathematical formulations of practically important financial problems.

For example, the following topics would be introduced with some assignments of computer programmings
1. Arbitrage free pricing theory
2. Binomial model
3. Black—Scholes model
4. Monte Carlo simulation / Discretization of stochastic differential equations
5. Overview of Malliavin calculus and its applications

Student learning outcomes

・Understand how the probability theory and the mathematical finance are used in the financial institution
・Be able to survey the recent hot topics of mathematical finance
・Get conscious about linkages of pure mathematics to the real world

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 quants.
Base on my professional experience as a derivative quant in the financial industry, I'll give some examples that theory of Mathematical finance is effective in practice.


Mathematical finance, Derivative quant, Arbitrage free pricing theory, Stochastic Differential Equation, Monte Carlo simulation, 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 is a standard lecture course with the presentation slides and black boards. There will be some assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Arbitrage free pricing theory Details will be provided during each class
Class 2 Foundation of stochastic differential equations and mathematical finance Details will be provided during each class
Class 3 Foundation of computational finance Details will be provided during each class
Class 4 Practical computational finance Details will be provided during each class
Class 5 Examples of application of modern math Details will be provided during each class


Details will be provided during each class session

Reference books, course materials, etc.

Details will be provided during each class session

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.C361 : Probability Theory
  • MTH.C507 : Advanced topics in Analysis G1
  • MTH.C508 : Advanced topics in Analysis H1

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

None in particular

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