A Problem in Making Resources Last

An individual uses up a certain resource at a constant rate, but from time to time has a chance to gamble some of the resource in order to gain more. The expectation of each gamble is zero, i.e., the gambles are fair. This means that eventually the resource will run out. However, the form of the risk can be varied arbitrarily. The question is what form of risk to choose, when the object is maximize the expectation of the utility, u(T), of having the resources run out at time T. This problem is solved for a more or less arbitrary function u(T).

Various possible interpretations of such a function u(T) are discussed briefly.

The model is mainly intended to provide a basis for empirical studies of individual decision making, where its complete mathematical tractibility is convenient.