Kostas Kardaras (Boston University)

Tittle: Numeraire-invariant choices in financial modeling

Abstract: 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 log-investment with a random-time horizon.

If time permits, further applications of the representation of optional measures with unit mass in the theory of random times will be
given. This last topic is work in progress.