Economic Survival Under Uncertainty

In this talk, I shall discuss some models of economic behavior under uncertainty in which survival an important-if not sole-objective of the economic agent. In the first model, the agent continuously reallocates his capital among investments that each yield a stochastic rate of return. The agent is constrained, however, to pay out (or alternative, consume) a constant sum per unit of time. Failure occurs (if ever) the first time that the agent's capital falls to zero. 

The agent's objective is to maximize the expected discounted time to failure. I shall describe some partial results concerning the agent's optimal policy. For example, in the limiting case in which the agent's discount rate is zero, and the set of available investments includes some with positive expected rates of return, then a complete solution is obtained for any set of investments satisfying this condition. The policy has the striking feature that the agent exhibits 'risk-loving' or 'risk-averse' behavior according as his capital is above or below critical level.