GCOE特別講義 "Introduction to Optimal Stopping in Discrete Time" (2009年11月16日〜19日)

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)


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