Optimal stopping (reference request)

Question

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?

score 6 · Accepted Answer · edited Apr 05 '22 at 14:34

6

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.

edited Apr 05 '22 at 14:34

Herr K.

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answered Apr 05 '22 at 13:06

Michael Greinecker

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Thanks for this! Are there any textbooks on this that you especially recommend? – afreelunch Apr 05 '22 at 16:01
I don't have any special recommendations, but the book "Recursive Macroeconomic Theory" by Ljungqvist and Sargent discusses the model. – Michael Greinecker Apr 05 '22 at 21:10

Optimal stopping (reference request)

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