APPROXIMATION OF STOCHASTIC INTEGRALS WITH JUMPS VIA WEIGHTED BMO APPROACH

• 成果类型: Article
• 署名作者: Thuan, Nguyen tran
• 署名单位: Saarland University; Vinh University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2075
• 发表日期: 2024
• 页码: 4595-4634
• 关键词: driven; Discretization; CONVERGENCE

摘要

This article investigates discrete-time approximations of stochastic integrals driven by semimartingales with jumps via weighted bounded mean osfor the approximation error depending on the weight, and it allows a change of the underlying measure which leaves the error estimates unchanged. To take advantage of this approach, we propose a new approximation scheme obtained from an adjustment for the Riemann approximation based on tracking jumps of the underlying semimartingale. We discuss a way to optimize the approximation and also illustrate the sharpness of the obtained convergence rates. When the small jump activity of the semimartingale behaves like an alpha-stable process with alpha is an element of (1, 2), our scheme achieves under a regular regime the same convergence rate for the error as in Rosenbaum and Tankov [Ann. Appl. Probab. 24 (2014) 1002-1048]. Moreover, our approach extends to the case alpha is an element of (0, 1] and to the Lp-setting which are not treated there. As an application, we apply the methods in the special case where the semimartingale is an exponential L & eacute;vy process to mean-variance hedging of European type options.