  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.
