REPLICATION OF AMERICAN CONTINGENT CLAIMS IN INCOMPLETE MARKETS

Abstract

The problem of hedgeability and replicatability of American contingent claims is discussed in an incomplete market. Here the incompleteness of the market is due to the possible degeneracy of the volatility matrix. Using the idea of the four-step scheme and penalization for a class of nonlinear backward stochastic differential equations, we prove, under proper conditions, that the so-called s-hedgeable American contingent claims are replicatable.