Numbering Code	P-MGT75 60399 LJ43	Year/Term	2022 ・ First semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Wed.5
Instructor name	Rusudan Kevkhishvili (Graduate School of Economics Senior Lecturer)
Outline and Purpose of the Course	In this course, students will study probability theory and stochastic processes systematically. The content of this lecture provides the foundation for research in financial engineering as well as other fields (mathematics, engineering, etc.) which utilize stochastic processes. This course is mainly aimed at students who aspire to become researchers and includes technical mathematical content.
Course Goals	By completing this course, students will understand the fundamentals of probability theory.
Schedule and Contents	Topics covered in this course are as follows: Weeks 1-2 Measure space and measurable functions Weeks 3-4 Integration theory Week 5 Probability measure, random variable, and distribution function Weeks 6-7 Expectation and uniform integrability Week 8 Product spaces Week 9 Conditional expectation Weeks 10-11 Convergence　　 Week 12 Stochastic processes, filtrations, and stopping times Weeks 13-14 Martingales in discrete time Week 15 Feedback
Evaluation Methods and Policy	Grades will be reported as row scores on a scale of 100 points. Evaluation methods and weights: Homework (50%), Final Exam (50%)
Course Requirements	・Knowledge of mathematical analysis and calculus (limit operations, differentiation, integration, etc.) ・Ability to spend sufficient time on homework and review
Study outside of Class (preparation and review)	Review of the course materials is mandatory. Students should also preview the content of each class.
Textbooks	Textbooks/References	Probability and Stochastics, Erhan Cinlar, (Springer), ISBN:978-0-387-87858-4