<p>I recommend the manuscript <a href="https://math.berkeley.edu/~evans/control.course.pdf" rel="nofollow">here</a> by Lawrence Evans. The related example is described as 'Rocket Railroad Car'. The first instance is on pages 9-12 where a geometric solution is provided. The choice set is not constrained to a discrete set in principle but the first part shows optimality when only the highest and lowest actions are chosen. On pages 35-36, Evans is proving that the geometric approach results in the correct solution, i.e. the discrete solution arises endogenously. Therefore, the remark is that you can consider a wider choice set and end up showing that the solution with discrete choices is also a solution when a larger choice set is considered.</p>

CC BY-SA 3.0
2015-09-29T00:23:16.770Z
2015-09-29T00:23:16.770Z
ramazan
<p>When we solve Bellman equations, I normally would think of the Blanchard Kahn technique. But in the case that I have an optimal stopping problem, or where the decision that the agent has to take is to choose the maximum from  two alternatives , I am not sure about how am I supposed to solve/proceed. There is no Euler equation  because the problem is discrete. Any suggestions are welcome. Thanks!</p>

<macroeconomics><optimal-control><bellman-equations>
Optimal Stopping
ChinG
# Optimal Stopping

(Asked by: username_0 on 2015-09-28)

When we solve Bellman equations, I normally would think of the Blanchard Kahn technique. But in the case that I have an optimal stopping problem, or where the decision that the agent has to take is to choose the maximum from two alternatives , I am not sure about how am I supposed to solve/proceed. There is no Euler equation because the problem is discrete. Any suggestions are welcome. Thanks!

**Tags:** macroeconomics, optimal-control, bellman-equations

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## 1 answers

### Answer by username_1 on 2015-09-29. Score: 2 | Accepted answer

I recommend the manuscript [here](https://math.berkeley.edu/~evans/control.course.pdf) by Lawrence Evans. The related example is described as 'Rocket Railroad Car'. The first instance is on pages 9-12 where a geometric solution is provided. The choice set is not constrained to a discrete set in principle but the first part shows optimality when only the highest and lowest actions are chosen. On pages 35-36, Evans is proving that the geometric approach results in the correct solution, i.e. the discrete solution arises endogenously. Therefore, the remark is that you can consider a wider choice set and end up showing that the solution with discrete choices is also a solution when a larger choice set is considered.


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