Optimal Stopping


Given a stochastic process in some filtered probability space and a time horizon, determine the stopping time to maximize the gain (e.g. largest value).

Secretary Problem

Need to choose a secretary amongst a list of candidates. Once a candidate is rejected, can’t be brought back, and must immediately respond to the candidate hire/pass after the interview. At what point should we choose a candidate?

  1. Choose a sample size that effectively acts as our benchmark. Too small: not enough information. Too large: burned through most of the candidates. Optimal sample size is n / e (n=number_candidates; e=2.71828)
  2. Choose the next number that is larger than the top candidate in n/e

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