We provide an axiomatic foundation for the representation of numeraire-invariant preferences of  agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following 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 is extended to expected logarithmic utility maximization . We also discuss the previous in a dynamic environment, where consumption streams are the objects of choice. There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. Finally, we give an application to the problem of optimal numeraire investment with a random-time horizon .
We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following 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 objects of choice. There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. Finally, we give an application to the problem of optimal numeraire investment with a random time-horizon .
A
economic
R
is extended to
has an extension that can be numerically represented by
D
maximization
R
discuss the previous in
treat the case of
R
optional measures with unit mass enables one
unit-mass optional measures enables
D
completely
R
random-time horizon
random time-horizon