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I've got a very basic question about optimal stopping. It may have just been me, but I feel like my professor didn't do a great job of explaining the topic too well. I was hoping one of you would be able to step me through this simple example:

Consider a simple random walk with absorbing boundaries on {0, 1, 2, ..., 10}. Suppose the following payoff function is given

$$[0, 2, 4, 3, 10, 0, 6, 4, 3, 3, 0].$$

Find the optimal stopping rule and give the expected payoff starting at each site.

Any help is greatly appreciated. Thanks!

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    Reference: This is Exercise 4.1 (page 98) in Gregory Lawler's "Introduction to Stochastic Processes (2nd edition)".2014-04-25

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