Optimal Stopping
Resources
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?
- 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) - Choose the next number that is larger than the top candidate in n/e