We consider a discrete-time linear state equation with delay, which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain alpha and a sequence v(k), which models asset returns that are within known bounds but otherwise arbitrary. We introduce two thresholds, alpha- and alpha(+), depending on these bounds, and prove that for alpha < alpha-, state positivity is guaranteed for all time and all asset-return sequences, i.e., bankruptcy is ruled out and positive solutions of the state equation are continuable indefinitely. On the other hand, for alpha > alpha(+), we show that there is always a sequence of asset returns for which the state fails to be positive for all time, i.e., along this sequence, bankruptcy occurs and the solution of the state equation ceases to be meaningful after some finite time. Finally, this article also includes a conjecture, which says that for the "gap" interval alpha- <= alpha <= alpha(+), state positivity is also guaranteed for all time. Support for the conjecture, both theoretical and computational, is provided.