Continuity Properties of Optimal Multiple Stopping Value |
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Authors: | Teruo Tanaka |
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Institution: | 1. Department of Systems Engineering, Graduate School of Information Sciences , Hiroshima City University , Hiroshima, Japan teruo@hiroshima-cu.ac.jp |
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Abstract: | This article is concerned with the optimal multiple stopping problem for discrete time finite stage stochastic processes. We study lower semicontinuity and continuity properties of optimal stopping values with respect to the topology of convergence in distribution. Also, we formulate the multiple stopping version of the prophet inequality for the optimal stopping problem and apply the lower semicontinuity property of optimal stopping values to the prophet inequality for the optimal multiple stopping problem. |
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Keywords: | Convergence in distribution Lower semicontinuity Optimal multiple stopping Prophet inequality Triangular function |
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