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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?

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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.

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  • $\begingroup$ 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. $\endgroup$
    – Michael Greinecker
    Apr 5, 2022 at 21:10

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