  We propose a new approach to solving dynamic decision problems with rewards
that are unbounded below. The approach involves transforming the Bellman
equation in order to convert an unbounded problem into a bounded one. The major
advantage is that, when the conditions stated below are satisfied, the
transformed problem can be solved by iterating with a contraction mapping.
While the method is not universal, we show by example that many common decision
problems do satisfy our conditions.
