Utility-Based Utility : The Johnsen-Donaldson Hypothesis

A major virtue of von Neumann-Morgenstern utility, for example, in the theory of general financial equilibrium (GFE), is that it ensures time consistency: consumption-portfolio plans (for the future) are in fact executed (in the future) - assuming that there is perfect foresight about relevant endogenous variables. This note examines an alternative to expected utility, one which also delivers consistency between plan and execution - and more. In particular, it turns out that one special case is in fact simply discounted expected utility. Moreover, this alternative formulation affords an extremely hospitable setting for introducing extrinsic uncertainty. The key idea behind the approach is to divorce the concept of filtration (of the state space) from any considerations involving probability (on the state space), and then to concentrate attention on nested utilities of consumption looking forward from any date-event: utility today depends only on consumption today and prospective utility tomorrow, utility tomorrow depends only on consumption tomorrow and prospective consumption the day after tomorrow, and so on