Work

Error distributions for random grid approximations of multidimensional stochastic integrals

Year: 2013

Type: article

Abstract: 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.

Source: The Annals of Applied Probability

DOI: 10.1214/12-aap858

Authors: Carl Lindberg, Holger Rootzén

Institutions: Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Stiftelsen för Strategisk Forskning

OpenAlex ID: W2014476361