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授業の目的 【日本語】
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授業の目的 【英語】
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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.
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到達目標 【日本語】
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到達目標 【英語】
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Understand the basics of stochastic processes and of Ito calculus.
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授業の内容や構成
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Course content:
Mathematical Background
Gaussian processes
Brownian motion
Stochastic integrals
Ito processes and stochastic differential equations
Markov processes
Applications to finance
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履修条件
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Knowledge on standard undergraduate linear algebra, calculus and advanced calculus.
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関連する科目
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Any course on probability and stochastic processes.
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成績評価の方法と基準
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Grades based on attendance and on written reports. An active participation of the students is desirable.
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教科書・テキスト
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Lecture notes will be provided during the lectures.
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参考書
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[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
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課外学習等（授業時間外学習の指示）
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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.
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注意事項
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他学科聴講の可否
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他学科聴講の条件
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This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome.
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レベル
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キーワード
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Stochastic processes, Brownian motion, Ito calculus, Black-Scholes model.
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履修の際のアドバイス
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授業開講形態等
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Face-to-face in room 309 of the math building.
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遠隔授業（オンデマンド型）で行う場合の追加措置
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