Transaction costs preclude the construction of hedging strategies
for general contingent claims. Leland introduced the concept of diffusion
limits of hedging strategies in a small transaction cost limit. This paper
establishes such diffusion limits for very general hedging strategies and also
establishes leading order asymptotic expressions for the replication error. In
addition to subsuming previously considered temporal strategies, the results in
this paper yield new results, namely expressions for replication errors of
stock price strategies and a variety of "renewal" strategies. Most
importantly, this paper provides a unified methodology for calculating hedging
strategies and replication errors in the small transaction cost limit. This is
an essential component of optimization methods, when, for example one is trying
to minimize replication error for a given initial portfolio value.