On martingale measures when asset returns have unpredictable jumps
type: Item
instance of: scholarly article
title: On martingale measures when asset returns have unpredictable jumps
zbMATH Open document ID: 0870.90016
DOI: 10.1016/0304-4149(96)00061-0
author: Indrajit Bardhan
author: Xiuli Chao
published in: Stochastic Processes and their Applications
publication date: 1997-08-07T00:00:00Z
review text: The paper studies incompleteness in financial markets induced by discontinuities in asset returns. The uncertainty is present not only in the timing of the jump but in the jump size as well. It is shown that, differently from the pure diffusion case or the case of predictable jump sizes, contingent claims cannot be either hedged completely or fairly priced by arbitrage. However, the authors identify a family of martingale measures that arise from arbitrage considerations. Each of these measures is a price functional in some auxiliary market, although, even in the markets so augmented, full hedging is still impossible. Therefore, the martingale measures only supply a bound on the price of the claim.
reviewed by: Alexis Derviz
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1046568
zbMATH Keywords: unpredictable jumps
zbMATH Keywords: incomplete market
zbMATH Keywords: contingent claim
MaRDI profile type: Publication
full work available at URL: 0304-4149(96)00061-0
OpenAlex ID: W1986560609
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description: scientific article; zbMATH DE number 1046568