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