学部・大学院区分
Undergraduate / Graduate		多・博前
時間割コード
Registration Code		3211087
科目区分
Course Category		Ａ類Ⅱ（専門科目）
Category A-2
科目名　【日本語】
Course Title		数理科学特論Ⅰ
科目名　【英語】
Course Title		Topics in Mathematical ScienceⅠ
コースナンバリングコード
Course Numbering Code
担当教員　【日本語】
Instructor		RICHARD Serge charles ○
担当教員　【英語】
Instructor		RICHARD Serge charles ○
単位数
Credits		2
開講期・開講時間帯
Term / Day / Period		春 水曜日 １時限
Spring Wed 1
授業形態
Course style
学科・専攻
Department / Program
多元数理科学研究科
必修・選択
Required / Selected
選択


授業の目的　【日本語】
Goals of the Course(JPN)
See English version
授業の目的　【英語】
Goals of the Course
Title: Introduction to stochastic calculus

The The aim of this course is to understand the basics of stochastic calculus, and to look applications in finance. Other applications will be studied depending on the interest of the audience.
到達目標　【日本語】
Objectives of the Course(JPN))
See English version.
到達目標　【英語】
Objectives of the Course
Understand the basics of stochastic processes and of Ito calculus.
授業の内容や構成
Course Content / Plan
Course content:

Mathematical Background
Gaussian processes
Brownian motion
Stochastic integrals
Ito processes and stochastic differential equations
Markov processes
Applications to finance
履修条件
Course Prerequisites
Knowledge on standard undergraduate linear algebra, calculus and advanced calculus.
関連する科目
Related Courses
Any course on probability and stochastic processes.
成績評価の方法と基準
Course Evaluation Method and Criteria
Grades based on attendance and on written reports. An active participation of the students is desirable.
教科書・テキスト
Textbook
Lecture notes will be provided during the lectures.
参考書
Reference Book
[A] J.-L. Arguin, A first course in stochastic calculus
[B] P. Baldi, Stochastic calculus, an introduction through theory and exercises
[D] R. Durrett, Stochastic calculus, a practical introduction
[E] L.C. Evans, An introduction to stochastic differential equations
[K] F. Klebaner, Introduction to stochastic calculus with applications
[Ku] H.-H. Kuo, Introduction to stochastic integration
[M] T. Mikosch, Elementary stochastic calculus with finance in mind
[SP] R. Schilling; L. Partzsch, Brownian Motion: an introduction to stochastic processes
課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours)
Students are supposed to read their notes between two lectures. The subjects of the reports can be chosen according to the interest of the students.
注意事項
Notice for Students
Additional information and material will be added regularly on

http://www.math.nagoya-u.ac.jp/~richard/Stochastic.html
他学科聴講の可否
Propriety of Other department student's attendance
他学科聴講の条件
Conditions of Other department student's attendance
This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome.
レベル
Level
2
キーワード
Keyword
Stochastic processes, Brownian motion, Ito calculus, Black-Scholes model.
履修の際のアドバイス
Advice
授業開講形態等
Lecture format, etc.
Face-to-face in room 309 of the math building.
遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class)