| Abstract: | In this paper, we study the replication of options in security markets X with a finite number of states. Specifically, we prove that in security markets without binary vectors, for any portfolio, at most m ? 3 options can be replicated where m is the number of states. This is an essential improvement of the result of Baptista where it is proved that the set of replicated options is of measure zero. Additionally, we extend the results of Aliprantis and Tourky on the nonreplication of options by generalizing their condition that markets are strongly resolving. Our results are based on the theory of lattice‐subspaces and positive bases. |
