Economy – Quantitative Finance – General Finance
Scientific paper
2009-03-22
Annals of Applied Probability 2010, Vol. 20, No. 5, 1697-1728
Economy
Quantitative Finance
General Finance
Published in at http://dx.doi.org/10.1214/09-AAP669 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/09-AAP669
We provide an axiomatic foundation for the representation of num\'{e}raire-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 us 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 num\'{e}raire investment with a random time-horizon.
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