Open Access
August 2011 Discretization error of stochastic integrals
Masaaki Fukasawa
Ann. Appl. Probab. 21(4): 1436-1465 (August 2011). DOI: 10.1214/10-AAP730

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.

Citation

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Masaaki Fukasawa. "Discretization error of stochastic integrals." Ann. Appl. Probab. 21 (4) 1436 - 1465, August 2011. https://doi.org/10.1214/10-AAP730

Information

Published: August 2011
First available in Project Euclid: 8 August 2011

zbMATH: 1234.60024
MathSciNet: MR2857453
Digital Object Identifier: 10.1214/10-AAP730

Subjects:
Primary: 60F05 , 60F17 , 60H05

Keywords: discrete hedging , Euler–Maruyama scheme , stable convergence

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.21 • No. 4 • August 2011
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