A super-replication theorem in Kabanov's model of transaction costs
The authors prove a general super-replication theorem for bid-ask processes that are not necessarily continuous. The notions of admissible predictable portfolio process and of a strictly consistent price system (SCPS) are developed. The main result states that if there exists an SCPS then the set of attainable contingent claims is Fatou-closed with respect to the order induced by the final solvency cone. This means that it is possible to pass from a sequence of portfolio processes that are uniformly bounded from below to a limiting portfolio process. A central tool is a generalized and parameterised version of Helly's theorem on pointwise convergence for sequences of functions of uniformly bounded variation.
scientific article; zbMATH DE number 5158702