Abstract
The optimal policy and the value function of a problem of optimal switching between a Wiener process and a deterministic motion on a segment are found in the present article. The speed of the motion is equal to 1 and it is in direction to the nearest end of the segment. For every switching a positive payment has to be paid. The problem is to minimize the sum of the first exit time of the process and the total payment. It turns out that there exist four different optimal rules depending on the length of the segment and the switching cost.
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Donchev, D.S. An example of optimal switching between a wiener process and a deterministic motion with a non-zero switching cost. ZOR - Methods and Models of Operations Research 41, 57–70 (1995). https://doi.org/10.1007/BF01415065
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DOI: https://doi.org/10.1007/BF01415065