Intertemporal borrowing to sustain exogenous consumption standards under uncertainty

Consider an agent who is attempting to maintain a given consumption level over time, in the face of a stochastic technology. He is permitted to borrow and lend at given rates of interest. The main results are: (i) if the borrowing rate of interest exceeds the lending rate, the expected net indebtedness of the agent must grow unboundedly large, unless the consumption target is attainable with at most one loan, and (ii) the probabilities of the two events: becoming increasingly indebted, and accumulating unbounded wealth, sum to unity.