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An Optimal Selling Strategy Based on Predicting the Ultimate Maximum Price

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In this talk I will present an optimal selling strategy for an asset in the following sense. Suppose that an investor has a long position in one financial asset, whose price is modelled by some stochastic process. The investor’s objective is to determine a “best moment” at which to close out the position before a given time and to sell the asset at the highest possible price, i.e. as close as possible to the ultimate maximum price over the whole period. This optimal decision must be based on continuous observations of the asset price performance and only on the information accumulated to date. Hence, the investor should use a prediction of the future evolution of the price of the financial security. In the case where the asset price is modelled by a spectrally positive stable Levy process, we describe explicitly the optimal strategy under certain conditions on the model parameters. The optimal strategy is of the following form: the investor must stop the observation of the price process and sell the asset as soon as the associated reflected process crosses for the first time a particular stopping boundary. To this connection we need to derive also the law of the associated supremum process and the latter problem dates back to 1973. Finally we provide numerical estimates and simulation examples of the results obtained by using this strategy.

This talk is part of the Cambridge Finance Workshop Series series.

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