Discretization error of stochastic integrals

Abstract

Limit distributions for the error in approximations of stochastic integrals by Riemann sums with stochastic partitions are studied. The integrands and integrators are supposed to be one-dimensional continuous semimartingales. Lower bounds for asymptotic conditional üariance of the error are giüen and effectiüe discretization schemes which attain the bounds are explicitly constructed. Two examples of their applications are giüen; efficient delta hedging strategies under fixed or linear transaction costs and effectiüe discretization schemes for the Euler-Maruyama approximation are constructed. © 2011 Institute of Mathematical Statistics.