## MITACS Math Finance Seminar 2007

- Date: 01/17/2007

Joern Sass (Austrian Academy of Sciences Linz, Austria)

University of British Columbia

We study the existence of a numeraire portfolio for a discrete time

financial market with proportional transaction costs. In an incomplete

market without frictions, consistent prices for derivative securities

can be obtained by taking the expectation of the claim with respect to

a certain probability measure under which the discounted asset prices

become martingales. The numeraire portfolio allows to replace this

change of measure by a change of numeraire. For models with transaction

costs, the concept of a martingale measure and thus the concept of a

numeraire portfolio have to be modified. Without transaction costs a

well known approach is to find the growth optimal portfolio (but the

numeraire portfolio might not exist). With some modifications and under

reasonable conditions the same approach turns out to work for our model.

MITACS Math Finance Seminar 2007