Before revision:  We generalize this problem by accounting for the effects of market impact, that is the fact that prices respond to trading activity. In particular, we assume that the value of an investment portfolio should be measured in terms of the cash-flow that can be generated by liquidating the portfolio, rather than by its mark-to-market value .
After revision:  We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance .