<p>This is known as the McCall search model in economics. The original paper shows that the optimal stopping strategy rule is given by a &quot;reservation wage&quot;, there is a threshold such that it is optimal to accept any draw above this threshold:</p>
<p>McCall, John J. &quot;<a href="https://www.jstor.org/stable/2351065" rel="nofollow noreferrer">The economics of information and optimal stopping rules</a>.&quot; <em>The Journal of Business</em> 38.3 (1965): 300-317.</p>

CC BY-SA 4.0
2022-04-05T16:01:30.527Z
Thanks for this! Are there any textbooks on this that you especially recommend?
afreelunch
CC BY-SA 4.0
2022-04-05T21:10:39.877Z
I don't have any special recommendations, but the book "Recursive Macroeconomic Theory" by Ljungqvist and Sargent discusses the model.
Michael Greinecker
CC BY-SA 4.0
2022-04-05T13:06:55.447Z
2022-04-05T14:34:42.720Z
2022-04-05T14:34:42.720Z
Michael Greinecker
<p>I am interested in the following optimal stopping problem:</p>
<ul>
<li>On each day, a number <span class="math-container">$a_i$</span> is drawn from a (possibly fixed) distribution.</li>
<li>I can either stop now, getting a payoff of <span class="math-container">$a_i$</span>, or wait for a later
draw.</li>
<li>In principle, this could go on forever. However, future payoffs are
discounted at a (possibly constant) rate.</li>
</ul>
<p>I know this kind of problem has been analysed extensively. Can anyone recommend some references on how one characterises optimal strategies in this context?</p>

<dynamic-programming>
Optimal stopping (reference request)
afreelunch
# Optimal stopping (reference request)

(Asked by: username_0 on 2022-04-05)

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?

**Tags:** dynamic-programming

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## 1 answers

### Answer by username_1 on 2022-04-05. Score: 6 | Accepted answer

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](https://www.jstor.org/stable/2351065)." *The Journal of Business* 38.3 (1965): 300-317.

> **Comments:**
> **username_0**: Thanks for this! Are there any textbooks on this that you especially recommend?  
> **username_1**: I don't have any special recommendations, but the book "Recursive Macroeconomic Theory" by Ljungqvist and Sargent discusses the model.  

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