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A note on completeness in large financial markets
Author(s) -
De Donno Marzia
Publication year - 2004
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2004.00193.x
Subject(s) - completeness (order theory) , financial market , arbitrage , gödel's completeness theorem , incomplete markets , economics , mathematical economics , mathematics , econometrics , financial economics , finance , discrete mathematics , microeconomics , mathematical analysis
We study completeness in large financial markets, namely markets containing countably many assets. We investigate the relationship between asymptotic completeness in the global market and completeness in the finite submarkets, under a no‐arbitrage assumption. We also suggest a way to approximate a replicating strategy in the large market by finite‐dimensional portfolios. Furthermore, we find necessary and sufficient conditions for completeness to hold in a factor model.