On the fundamental theorem of asset pricing with an infinite state space
type: Item
instance of: scholarly article
title: On the fundamental theorem of asset pricing with an infinite state space
zbMATH Open document ID: 0721.90016
DOI: 10.1016/0304-4068(91)90014-K
author: Kerry Back
author: Stanley R. Pliska
published in: Journal of Mathematical Economics
publication date: 1991-01-01T00:00:00Z
review text: An example is given of a securities market in which there are no arbitrage opportunities - moreover, a risk-neutral agent facing a nonnegative wealth constraint has an optimal trading strategy - yet there is no equivalent martingale measure and no state price density. This failure of the ``Fundamental Theorem of Asset Pricing'' is due to the fact that the pricing operator for \(L^{\infty}\) claims is not countably additive - it is a finitely additive measure with a nontrivial purely finitely additive component. Some new sufficient conditions are given for this measure to be countably additive.
Mathematics Subject Classification ID: 91B24
zbMATH DE Number: 4189434
zbMATH Keywords: countably additive measure
zbMATH Keywords: securities market
zbMATH Keywords: risk-neutral agent
zbMATH Keywords: optimal trading strategy
zbMATH Keywords: finitely additive measure
MaRDI profile type: Publication
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full work available at URL: 0304-4068(91)90014-k
OpenAlex ID: W2061270640
description: scientific article