  Asymptotic error distribution for approximation of a stochastic integral with
respect to continuous semimartingale by Riemann sum with general stochastic
partition is studied. Effective discretization schemes of which asymptotic
conditional mean-squared error attains a lower bound are constructed. Two
applications are given; efficient delta hedging strategies with transaction
costs and effective discretization schemes for the Euler-Maruyama approximation
are constructed.
