BFS 2002

Poster Presentation

A note on completeness in "large financial markets"

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 many assets. 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 assets. Finally, we characterize completeness in very simple factor models, where diversification allows to complete an otherwise incomplete market.