Abstract
In this paper, we develop an optimal stock selling strategy with the stochastic upper bound of selling rate over an infinite time horizon. Moreover, the temporary and permanent price impact are considered. We treat the problem by using a fluid model. In the model that the number of shares is treated as fluid (continuous) and the overall liquidation is dictated by the rates of selling over time. The goal is to maximize the overall return under state constraints. The corresponding value function with the selling strategies is shown to be continuous and the unique viscosity solution to the associated HJB equation. Finally, a numerical example is given to illustrate the result.
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