The Annals of Applied Probability

Discretization error of stochastic integrals

Masaaki Fukasawa

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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 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

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

Dates
First available in Project Euclid: 8 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1312818841

Digital Object Identifier
doi:10.1214/10-AAP730

Mathematical Reviews number (MathSciNet)
MR2857453

Zentralblatt MATH identifier
1234.60024

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

Keywords
Stable convergence discrete hedging Euler–Maruyama scheme

Citation

Fukasawa, Masaaki. Discretization error of stochastic integrals. Ann. Appl. Probab. 21 (2011), no. 4, 1436--1465. doi:10.1214/10-AAP730. https://projecteuclid.org/euclid.aoap/1312818841


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