The Structure of an Optimal Stopping Problem

Many aspects of the financial world are implicitly modeled using optimal stopping under the hood. In your case, you encountered a real life example where the assumptions of the model were a little bit relaxed in the case of making that higher. You were able to go back and extend an offer to someone even if you didn't hire them on the spot. There are optimal algorithms for this version of the problem too, which is known as recall, trading.

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