A proof of the Dalang-Morton-Willinger theorem

Abstract

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.

9 pages

References in corpus (2)

• Lower bounds of martingale measure densities in the Dalang-Morton-Willinger theorem
• Kreps-Yan theorem for Banach ideal spaces