Most of the investments in practice are carried out without certain horizons. There are manyfactors to drive investment to a stop. In this paper, we consider a portfolio selection policy withmarket-related stopping time. Particularly, we assume that the investor exits the market once hiswealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is tominimize the expected time when the investment target is obtained, at the same time, we guaranteethe probability that bankruptcy happens is no larger than a given level. We formulate the problemas a mix integer linear programming model and make analysis of the model by using a numericalexample.
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