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BAYESIAN OPTIMAL STOPPING PROBLEMS WITH PARTIAL
INFORMATION
by
Yen-Ming Lee
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)
December 2010
Copyright 2010 Yen-Ming Lee
Object Description
| Title | Bayesian optimal stopping problems with partial information |
| Author | Lee, Yen-Ming |
| Author email | yenmingl@usc.edu; leemiho@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Industrial & Systems Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2010-12 |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-11-22 |
| Advisor (committee chair) | Ross, Sheldon M. |
| Advisor (committee member) |
Dessouky, Maged M. Moore, James Elliott, II. Marino, Anthony M. |
| Abstract | This dissertation focuses on an application of stochastic dynamic programming called the optimal stopping problem. The decision maker has to choose a time to take a given action based on sequentially observed random variables in order to maximize an expected payoff. All previous research on optimal stopping assumes that the distributions of random variables are completely known or partially known with unknown parameters. Throughout the dissertation, we address the problems with the uncertainty assumption that the random variables are from one of two possible distributions with given initial probabilities as to which is the true distribution. The probabilities are then updated in a Bayesian manner as the successive random variables are observed.; We first consider a problem of optimal stopping called asset-selling problem. There is a sequence of offers that comes in from a fixed but unknown distribution. The decision maker has to decide to take an offer or continue to observe the next offer. There is a fix cost for each offer observed. We consider both the cases where recalling a past offer is allowed and not allowed. Under our uncertainty assumption, the optimal solutions cannot be attained numerically. For each case, we present a dynamic programming model and present some structural results of the optimal policy. We propose some heuristic policies and upper bounds of the optimal expected return. Using simulation, the performances of the heuristic methods are evaluated by comparing with the upper bounds.; We study a variant of the asset-selling problem in which the decision now is to set up a reserve price before offers come in. The seller accepts an offer if and only if it is greater than the reserve price. The problem can be viewed as an eBay-like online auction problem if we consider the maximal bidding price of each auction as an offer. We develop a dynamic programming model and show that the optimal solution can be obtained by linear programming.; We then extend the work to another typical optimal stopping problem - the burglar problem. The problem considers a burglar who plans a series of burglaries. He/she may accumulate his/her earnings as long as he is not caught. If he/she is caught during a burglary, he/she loses everything and goes to jail. He/she wants to retire with a maximum expected fortune before he/she is caught. We again address the problem with our uncertainty assumption on the distribution of the returns for each burglary. There are two possible sets of the combination of the probability of a successful burglary and the loot distribution. We present the dynamic programming model and some structural results of the optimal policy. Some efficient heuristic policies are evaluated by comparing with the upper bounds of the optimal expected return. |
| Keyword | dynamic programming; optimal stopping; Bayesian updating |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3542 |
| Contributing entity | University of Southern California |
| Rights | Lee, Yen-Ming |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-Lee-4214 |
| Archival file | uscthesesreloadpub_Volume32/etd-Lee-4214.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | BAYESIAN OPTIMAL STOPPING PROBLEMS WITH PARTIAL INFORMATION by Yen-Ming Lee A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (INDUSTRIAL AND SYSTEMS ENGINEERING) December 2010 Copyright 2010 Yen-Ming Lee |
