A general version of the fundamental theorem of asset pricing
type: Item
instance of: scholarly article
title: A general version of the fundamental theorem of asset pricing
zbMATH Open document ID: 0865.90014
DOI: 10.1007/BF01450498
author: Freddy Delbaen
author: Walter Schachermayer
published in: Mathematische Annalen
publication date: 1994-12-11T00:00:00Z
full work available at URL: https://eudml.org/doc/165264
review text: The fundamental theorem of asset pricing is that for a stochastic process \(S=(S_t)_{t\in\mathbb{R}}\), the existence of an equivalent martingale measure is essentially equivalent to the absence of arbitrage opportunities. The present paper focuses on the term essentially in the above statement. The general idea underlying the no arbitrage condition is that there should be no trading strategy \(H\) for the process \(S\) such that the final payoff described by the stochastic integral \((H.S)_\infty\) is a nonnegative function strictly positive with positive probability which has been termed as the no free lunch with vanishing risk (NFLVR). The major result of this paper is contained in the following: Let \(S\) be a bounded real valued semi-martingale. There is an equivalent martingale measure for \(S\) if and only if \(S\) satisfies NFLVR. The fact that NFLVR guarantees the existence of an equivalent martingale measure for \(S\) allows wide applicability of martingale theory. Several versions of the no free lunch condition are also introduced and their relationship studied.
reviewed by: Anjan Mukherji
Mathematics Subject Classification ID: 91G99
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 701010
zbMATH Keywords: asset pricing
zbMATH Keywords: stochastic process
zbMATH Keywords: equivalent martingale measure
zbMATH Keywords: no arbitrage condition
zbMATH Keywords: no free lunch
Wikidata QID: Q56270295
MaRDI profile type: Publication
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OpenAlex ID: W4244967830
description: scientific article; zbMATH DE number 701010