e would like to derive conditions for the vector
to be unique.
The defining relationship is (we omit the upper index
To have uniqueness we must make sure that
is the notation for null set. In
hence, it is enough to show that
has the full range.
We introduce the notion of acceptable completeness.
The market is acceptably complete iff any payoff
may be hedged with existing assets so that the remaining risk is
Hence, it is enough to make sure that
spans the full space. This means that the space of cash flows is at least as
rich as the structure of the test measures.
has the maximal rank, the pricing vector is unique iff the market is