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 sub-markets, 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.
Original languageEnglish
Pages (from-to)295-315
Number of pages21
JournalMathematical Finance
Publication statusPublished - 2004


  • Completeness
  • Cylindrical stochastic integration
  • Factor models
  • Large financial market
  • Self-financing portfolio


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