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M6—On Minimal Market Models and Minimal Martingale Measures

In: Contemporary Quantitative Finance

Author

Listed:
  • Hardy Hulley

    (University of Technology, School of Finance and Economics)

  • Martin Schweizer

    (ETH Zürich, Departement Mathematik, ETH-Zentrum)

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.

Suggested Citation

  • Hardy Hulley & Martin Schweizer, 2010. "M6—On Minimal Market Models and Minimal Martingale Measures," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 35-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03479-4_3
    DOI: 10.1007/978-3-642-03479-4_3
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