Necessary and sufficient conditions for the existence of the q-optimal measure

Details Necessary and sufficient conditions for the existence of the q-optimal measure Necessary and sufficient conditions for the existence of the q-optimal measure

2008-08-27

arxiv.org/abs/0808.3751v1

Mathematics

Probability

Scientific paper

This paper presents the general form and essential properties of the q-optimal measure following the approach of Delbaen and Schachermayer (1996) and proves its existence under mild conditions. Most importantly, it states a necessary and sufficient condition for a candidate measure to be the q-optimal measure in the case even of signed measures. Finally, an updated characterization of the q-optimal measure for continuous asset price processes is presented in the light of the counterexample appearing in Cerny and Kallsen (2006) concerning Hobson's (2004) approach.

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