I am interested in the following optimal stopping problem:

  • On each day, a number $a_i$ is drawn from a (possibly fixed) distribution.
  • I can either stop now, getting a payoff of $a_i$, or wait for a later draw.
  • In principle, this could go on forever. However, future payoffs are discounted at a (possibly constant) rate.

I know this kind of problem has been analysed extensively. Can anyone recommend some references on how one characterises optimal strategies in this context?


1 Answer 1


This is known as the McCall search model in economics. The original paper shows that the optimal stopping strategy rule is given by a "reservation wage", there is a threshold such that it is optimal to accept any draw above this threshold:

McCall, John J. "The economics of information and optimal stopping rules." The Journal of Business 38.3 (1965): 300-317.

  • $\begingroup$ Thanks for this! Are there any textbooks on this that you especially recommend? $\endgroup$
    – afreelunch
    Apr 5, 2022 at 16:01
  • $\begingroup$ I don't have any special recommendations, but the book "Recursive Macroeconomic Theory" by Ljungqvist and Sargent discusses the model. $\endgroup$ Apr 5, 2022 at 21:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.