On approximative solutions of multistopping problems
Abstract
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal $m$stopping curves for this limiting model are determined by differential equations of first order. A general approximation result is established which ensures convergence of the finite discrete time $m$stopping problem to that in the limit model. This allows the construction of approximative solutions of the discrete time $m$stopping problem. In detail, the case of i.i.d. sequences with discount and observation costs is discussed and explicit results are obtained.
 Publication:

arXiv eprints
 Pub Date:
 December 2011
 arXiv:
 arXiv:1201.0083
 Bibcode:
 2012arXiv1201.0083F
 Keywords:

 Mathematics  Probability
 EPrint:
 Published in at http://dx.doi.org/10.1214/10AAP747 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)