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Multiple buying or selling with vector offers

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

F. Thomas Bruss  and
Thomas S. Ferguson
F. Thomas Bruss*
Affiliation:
Université Libre de Bruxelles
Thomas S. Ferguson*
Affiliation:
University of California, Los Angeles
*
∗Postal address: Université Libre de Bruxelles, Département de Mathématique et Institut de Statistique, CP 210, B-1050 Brussels, Belgium. e-mail: tbruss@ulb.ac.be
∗Postal address: Université Libre de Bruxelles, Département de Mathématique et Institut de Statistique, CP 210, B-1050 Brussels, Belgium. e-mail: tbruss@ulb.ac.be
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Abstract

We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1, X2, · ··, be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, · ··, Nk, one for each component. The payoff is the sum over j of the jth component of minus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.

Keywords

OPTIMAL STOPPINGHOUSE-SELLINGJOB SEARCHCOSTDISCOUNTRECALLCONVEX SET FUNCTION

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 959 - 973
Copyright
Copyright © Applied Probability Trust 1997 

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