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.

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MITACS Math Finance Seminar 2007