中研院

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中央研究院統計科學研究所

學 術 演 講

講　題：Some Marked Stopping Problems

演講人：Prof. Sheldon M. Ross(University of Southern California, USA)

時　間：2007年10月31日(星期三)上午10:30-12:00

地　點：中央研究院統計科學研究所二樓交誼廳

※茶會：上午10：10統計所二樓交誼廳


Abstract

　　　In a marked stopping problem independent random variables Y(1), Y(2),
... are observed in sequence; after each observation the decision maker must
decide whether to mark that varaible or not. At some point the decision maker
stops observing and collects a return that depends on the sequence of values
that have been observed and the indices of those that have been marked. We
argue that if the return function is a convex and nondecreasing function of
each observation then the maximal expected return increases as the
variability of the distributions of the Y(i) increase.
　　　A particular marked stopping problem we are interested in is one where
we have k items to sell, with offers arriving sequentially.In one variation
each new offer is either marked or not, and the problem ends when k offers
have been marked. However, the return function is k times the minimal marked
offer minus c times the number of offers observed. In a second variation
there is no marking, but at some time we stop and sell all k items at the kth
highest price observed.
　　　In the preceding the offer distribution is assumed known. A Bayesian
model where it is unknown will also be discussed.

--
哇 ROSS耶@@


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