GCOE特別講義 "Introduction to Optimal Stopping in Discrete Time" を開講します。
日 時： 11月16日（月）〜19日（木） いずれも午後３時から
場 所： 数学教室（理学部３号館）108号室
講 師： Pieter Allaart 氏（North Texas 大学）
なお，京都大学大学院理学研究科の大学院生には，本講義を受講すれば数学・数理解析専攻数理解析系の数理科学特別講義として１単位が認定されます．
<Abstract>
This lecture series is intended for advanced undergraduate students and graduate students of mathematics, economics or finance having an interest in applied probability. Ideally, students must have taken at least a one-semester course in (calculus-based) probability and have some basic notion of Markov chains and random walks. Some knowledge of measure and integration theory is also helpful, but not required as the concepts that depend on measure theory will be explained also at an intuitive level.
<Lecture Plan>
Lecture 1
A famous open problem; Notation and terminology; The general optimal stopping problem; Finite horizon problems: backward induction
Lecture 2
Secretary problems: The classical secretary problem; Extensions and variations. Introduction to infinite-horizon stopping time problems
Lecture 3
The infinite horizon case: The house-selling problem; Pricing of American options
Lecture 4
Prophet inequalities and related problems: Proof of the classical prophet inequality; Optimal stopping with respect to different filtrations; Open problems