ERROR DISTRIBUTIONS FOR RANDOM GRID APPROXIMATIONS OF MULTIDIMENSIONAL STOCHASTIC INTEGRALS

• 成果类型: Article
• 署名作者: Lindberg, Carl; Rootzen, Holger
• 署名单位: Chalmers University of Technology; University of Gothenburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP858
• 发表日期: 2013
• 页码: 834-857
• 关键词: differential-equations; WEAK-CONVERGENCE; LIMIT-THEOREMS

摘要

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.