The article introduces novel explicit Milstein-type schemes for the Ait-Sahalia type model in mathematical finance. It addresses the challenges posed by superlinear growth and nonlinear drift, focusing on unconditionally positivity-preserving approximations. The proposed schemes achieve first-order strong convergence and mean-square error bounds without relying on high-order moment bounds. The theoretical analysis is supported by numerical experiments validating the findings.
Introduction
Preliminaries
Proposed Explicit Scheme
Mean-Square Convergence Analysis
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by Yingsong Jia... at arxiv.org 03-26-2024
https://arxiv.org/pdf/2403.16975.pdfDeeper Inquiries