Error distributions for random grid approximations of multidimensional stochastic integrals
Artikel i vetenskaplig tidskrift, 2013

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.

multidimensional stochastic differential

weak-convergence

Approximation error

joint weak convergence

random grid

limit-theorems

differential-equations

Författare

CARL LINDBERG

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Holger Rootzen

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Annals of Applied Probability

1050-5164 (ISSN)

Vol. 23 834-857

Ämneskategorier

Matematik

DOI

10.1214/12-AAP858