A proof of the Dalang-Morton-Willinger theorem

Details A proof of the Dalang-Morton-Willinger theorem A proof of the Dalang-Morton-Willinger theorem

2008-04-21

arxiv.org/abs/0804.3308v1

Mathematics

Probability

9 pages

Scientific paper

We give a new proof of the Dalang-Morton-Willinger theorem, relating the no-arbitrage condition in stochastic securities market models to the existence of an equivalent martingale measure with bounded density for a $d$-dimensional stochastic sequence $(S_n)_{n=0}^N$ of stock prices. Roughly speaking, the proof is reduced to the assertion that under the no-arbitrage condition for N=1 and $S\in L^1$ there exists a strictly positive linear fucntional on $L^1$, which is bounded from above on a special subset of the subspace $K\subset L^1$ of investor's gains.

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