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April 2013 Error distributions for random grid approximations of multidimensional stochastic integrals
Carl Lindberg, Holger Rootzén
Ann. Appl. Probab. 23(2): 834-857 (April 2013). DOI: 10.1214/12-AAP858


This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue integrals of the integrands tend uniformly to zero and that the squared variation and covariation processes converge. The paper also provides tools which simplify checking these conditions and which extend the range for the results. These results are used to prove an explicit limit theorem for random grid approximations of integrals based on solutions of multidimensional SDEs, and to find ways to “design” and optimize the distribution of the approximation error. As examples we briefly discuss strategies for discrete option hedging.


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Carl Lindberg. Holger Rootzén. "Error distributions for random grid approximations of multidimensional stochastic integrals." Ann. Appl. Probab. 23 (2) 834 - 857, April 2013.


Published: April 2013
First available in Project Euclid: 12 February 2013

zbMATH: 1290.60025
MathSciNet: MR3059277
Digital Object Identifier: 10.1214/12-AAP858

Primary: 60F05 , 60H05 , 91G20
Secondary: 60G44 , 60H35

Keywords: Approximation error , discrete option hedging , joint weak convergence , multidimensional stochastic differential equation , portfolio tracking error , random evaluation times , random grid , stochastic integrals

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 2 • April 2013
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