**Walter Schachermayer**

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## A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time.

**W. Schachermayer**

Insurance: Mathematics and Economics, Vol. 11 (1992), pp. 249-257.

### Abstract:

R. Dalang, A. Morton and W. Willinger have proved a beautiful version
of the Fundamental Theorem of Asset Pricing which pertains to the
case of finite discrete time: In this case the absence of arbitrage
opportunities already characterizes the existence of an equivalent
martingale measure.

The purpose of this paper is to give an elementary
proof of this important theorem which relies only on orthogonality
arguments. In contrast, the original proof of Dalang, Morton and
Willinger uses heavy functional analytic machinery, in
particular measurable selection and measure-decomposition theorems. We feel that the
theorem (as well as its proof) should be accessible to a wider
public and we therefore
made an effort to keep the arguments as selfcontained as possible. In
a final chapter we review and prove the necessary tools for our
presentation of the theorem.

### Preprints:

[PostScript (231 k)] [PS.gz (91 k)] [PDF (267 k)] [DOI: 10.1016/0167-6687(92)90013-2 (0 k)]

Publications marked with have appeared in refereed journals.

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