MITACS Math Finance Seminar 2007

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.