Journal Title
Title of Journal: Decisions Econ Finan
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Abbravation: Decisions in Economics and Finance
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Authors: Jörn Sass Manfred Schäl
Publish Date: 2012/06/05
Volume: 37, Issue: 2, Pages: 195-234
Abstract
In a discretetime incomplete financial market with proportional transaction costs and with independent and bounded returns we prove the existence of a consistent price system that can be written as the expectation of the discounted claim under the realworld probability measure P and not just under a martingale measure In fact the claim is then discounted by some specific dynamic portfolio called the numeraire portfolio as in the classical case of markets without transaction costs For that specific numeraire P will be a martingale measure Naturally the concept of a numeraire portfolio has here to be adapted to the concept of consistent price systems for markets with transaction costs Moreover again as in the classical case the numeraire portfolio can be chosen as logoptimal portfolio The same analysis works for power utility functions However then a change of measure is necessary This paper applies methods from stochastic dynamic programming to finance
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