Probability criterion for a dynamic financial model with short-selling allowed

Probability criterion has its practical significance, and its investment decision-making is determined by the expected discounted wealth. In a complete, standard financial market with short-selling allowed, this paper probes into the investment decision-making with probability criterion. The upper limit of criterion function is obtained. The corresponding discounted wealth process and hedging portfolio process are provided. Finally, an illustrative example of one-dimensional constant-coefficient financial market is given.