NUMÉRAIRE-INVARIANT PREFERENCES IN FINANCIAL

We provide an axiomatic foundation for the representation of numéraire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the follow-ing choice rule: the agent prefers one outcome over another if and only if the expected (under the agent’s subjective probability) relative rate of return of the latter outcome with respect to the former is nonpositive. With the addition of a transitivity requirement, this last preference relation has an extension that can be numerically represented by expected logarithmic utility. We also treat the case of a dynamic environment where consumption streams are the ob-jects of choice. There, a novel result concerning a canonical representation of unit-mass optional measures enables us to explicitly solve the investment– consumption problem by separating the two aspects of investment and con-sumption. Finally, we give an application to the problem of optimal numéraire investment with a random time-horizon. 0. Introduction. Within the class of expected utility maximization problem