M6—On Minimal Market Models and Minimal Martingale Measures

Hardy Hulley () and Martin Schweizer ()
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Hardy Hulley: University of Technology, School of Finance and Economics
Martin Schweizer: ETH Zürich, Departement Mathematik, ETH-Zentrum

A chapter in Contemporary Quantitative Finance, 2010, pp 35-51 from Springer

Abstract: 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: Structure Condition; Asset Price; Martingale Measure; Local Martingale; Bessel Process (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03479-4_3

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DOI: 10.1007/978-3-642-03479-4_3

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