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.
De Donno, M., A note on completeness in large financial markets, <<MATHEMATICAL FINANCE>>, 2004; 14 (2): 295-315. [doi:10.1111/j.0960-1627.2004.00193.x] [http://hdl.handle.net/10807/168906]
A note on completeness in large financial markets
De Donno, Marzia
2004
Abstract
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.
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