The Annals of Applied Probability

Discretization error of stochastic integrals

Masaaki Fukasawa

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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 variance of the error are given and effective discretization schemes which attain the bounds are explicitly constructed. Two examples of their applications are given; efficient delta hedging strategies under fixed or linear transaction costs and effective discretization schemes for the Euler–Maruyama approximation are constructed.

Article information

Ann. Appl. Probab., Volume 21, Number 4 (2011), 1436-1465.

First available in Project Euclid: 8 August 2011

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles 60H05: Stochastic integrals

Stable convergence discrete hedging Euler–Maruyama scheme


Fukasawa, Masaaki. Discretization error of stochastic integrals. Ann. Appl. Probab. 21 (2011), no. 4, 1436--1465. doi:10.1214/10-AAP730.

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