Special lectures on current topics in Mathematics W

Academic unit or major

Graduate major in Mathematics

Instructor(s)

Yuji Shinozaki

Class Format

Lecture

Media-enhanced courses

-

Day of week/Period
(Classrooms)

Intensive

Class

-

Course Code

MTH.E654

Number of credits

200

Course offered

2021

Offered quarter

3Q

Syllabus updated

Jul 10, 2025

Language

Japanese

Syllabus

Course overview and goals

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

Course description and aims

・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

Student learning outcomes

実務経験と講義内容との関連 (又は実践的教育内容)

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.

Keywords

Mathematical finance, Derivative quant, Arbitrage free pricing theory, Stochastic Differential Equation, Monte Carlo simulation,　Malliavin calculus

Competencies

• 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/Objectives

Study advice (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)

Details will be provided during each class session.

Reference books, course materials, etc.

Details will be provided during each class session.

Evaluation methods and criteria

Assignments (100%).

Related courses

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

Prerequisites

None in particular