Abstract: Sharp asymptotic lower bounds of the expected quadratic
variation of discretization error in stochastic integration are given.
The theory relies on inequalities for the kurtosis and skewness of a
general random variable which are themselves seemingly new.
Asymptotically efficient schemes which attain the lower bounds are
constructed explicitly. The result is directly applicable to practical
hedging problem in mathematical finance; it gives an asymptotically
optimal way to choose rebalancing dates and portofolios with respect
to transaction costs. The asymptotically efficient strategies in fact
reflect the structure of transaction costs. In particular a specific
biased rebalancing scheme is shown to be superior to unbiased schemes
if transaction costs follow a convex model. The problem is discussed
also in terms of the exponential utility maximization.