Hedgeability and replicatability of European type contingent claims from controllability point of view

The problem of hedgeability and replicatability of European type contingent claims are discussed in an incomplete market with the wealth and the portfolio possibly being constrained. Such problems can be regarded as controllability problem for stochastic systems. For the case of no constraint, using the idea of the Four Step Scheme (Protter and Yong, 1994), we obtain the replicatability of a class of contingent claims (including European call and put options) without assuming ad hoc technical conditions. For the case with wealth and portfolio being constrained, several positive and negative results concerning the hedgeability and replicatability are presented