On the law of one price
type: Item
instance of: scholarly article
title: On the law of one price
zbMATH Open document ID: 1064.60084
author: Jean-Michel Courtault
author: Freddy Delbaen
author: Ch. Stricker
author: Yuri Kabanov
published in: Finance and Stochastics
publication date: 2005-05-20T00:00:00Z
review text: The authors study the law of one price (L1P) that is weaker than no arbitrage (NA) property of financial market. It can be formulated for one-period model as follows: the identity \(x+h\xi=x'+h'\xi\), where \(h,h'\in \mathbf R^d\), implies that \(x=x'\) (here \(\xi\in\mathbf R^d\) is a random vector describing price increments). In other words, if a contingent claim has a price, namely, a replication price, this price is unique. Clearly, this property is always fulfilled if NA holds. The aim of the paper is to analyze the law of one price for the multi-period model with a general probability space. The main result is that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. It is also shown that under such a weak condition as L1P the market portfolio exists.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 91G99
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91G10
zbMATH DE Number: 2169547
zbMATH Keywords: law of one price
zbMATH Keywords: Harrison-Pliska theorem
zbMATH Keywords: Dalang-Morton-Willinger theorem
zbMATH Keywords: market portfolio
zbMATH Keywords: CAPM
MaRDI profile type: Publication
full work available at URL: s00780-004-0124-9
OpenAlex ID: W2014688403
DOI: 10.1007/S00780-004-0124-9
description: scientific article; zbMATH DE number 2169547