Optimal stopping

Optimal stopping means choosing when to stop a process to get the best expected result for a stated goal, given the information and costs involved.

Secretary problem: a named example

In the classic secretary problem, you know how many candidates there are and want to choose one. They arrive in a random order, with every order equally likely. You can rank each candidate against those already seen, without ties, but do not know how that candidate ranks against those still to come. You must accept or reject each candidate on the spot, and a rejected candidate cannot return.

The aim is to maximize the probability of selecting the best candidate overall. Waiting may reveal a better candidate, but a good candidate you reject is lost.

Fundraising allows repeat meetings and negotiation. The problem helps frame the decision about when to stop searching, but its mathematical rule does not set a fundraising deadline.

Optimal stopping in practice

In Class 04, teams had limited meeting slots. Another meeting might help them find an investor, but time spent raising money also took time away from running businesses.

Where this comes from

The classroom example comes from Class 04: With Other People’s Money.

Concept reference: Thomas S. Ferguson, UCLA: Optimal Stopping and Applications, Chapter 2, section 2.1.

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