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Selling a stock at the ultimate maximum. (English) Zbl 1201.60037
The authors consider the problem of selling a stock at the ultimate maximum where the stock price follows geometric Brownian motion. They use two different formulations for this predictive problem and derive optimal strategies for both problems. The predictive problems are reduced to optimal stopping problems which are solved by using the methods of free boundary problems and local space-time calculus. Both solutions support the financial view that one should sell bad stocks and keep good ones.

MSC:
 60G40 Stopping times; optimal stopping problems; gambling theory 62L15 Optimal stopping in statistics 91G80 Financial applications of other theories 60J65 Brownian motion
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References:
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