Arlotto, AlessandroSteele, J. Michael2023-05-222023-05-222014-01-012017-08-25https://repository.upenn.edu/handle/20.500.14332/34551We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F, and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.This article has been published in a revised form in Advances in Applied Probability 10.1239/aap/1401369706. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press.Finance and Financial ManagementArticle