M6 - On Minimal Market Models and Minimal Martingale Measures

Hardy Hulley and Martin Schweizer
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Martin Schweizer: ETH Zurich and Swiss Finance Institute

No 280, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The well-known absence-of-arbitrage condition NFLVR from the fundamental theorem of asset pricing splits into two conditions, called NA and NUPBR. We give a literature overview of several equivalent reformulations of NUPBR; these include existence of a growth-optimal portfolio, existence of the numeraire portfolio, and for continuous asset prices the structure condition (SC). As a consequence, the minimal market model of E. Platen is seen to be directly linked to the minimal martingale measure. We then show that reciprocals of stochastic exponentials of continuous local martingales are time changes of a squared Bessel process of dimension 4. This directly gives a very specific probabilistic structure for minimal market models.

Keywords: minimal market model' minimal martingale measure; growth-optimal portfolio; numeraire portfolio; NUPBR, structure condition (SC); continuous local martingales; squared Bessel process of dimension 4; log-optimal portfolio (search for similar items in EconPapers)
Pages: 21 pages
Date: 2010-06-01
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Citations: View citations in EconPapers (49)

Published as: Hulley, H. and Schweizer, M., 2010, "M6 - On Minimal Market Models and Minimal Martingale Measures", In: Carl Chiarella and Alexander Novikov (eds) Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, 35-51.

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