Marzia De Donno
We analyze the question of completeness in a
market containing countably many asset.
In such a market portfolios involving an infinite
number of assets may be formed.
By making use of a cylindrical stochastic integral,
we define a notion of self-financing "generalized"
portfolio, as limit of "naive" portfolios,
where a "naive" portfolio is
instantaneously based on a finite number of assets,
while a generalized portfolio involves infinitely
The market is said to be complete if every
contingent claim can be replicated either by a generalized
portfolio or a naive portfolio.
We relate completeness in the large market to completeness
in the finite sub-markets and to completeness
on the set of claims depending on a finitely many
Finally, we characterize completeness in very
simple factor models,
where diversification allows to complete
an otherwise incomplete market.