ASYMPTOTICALLY OPTIMAL DISCRETIZATION OF HEDGING STRATEGIES WITH JUMPS

• 成果类型: Article
• 署名作者: Rosenbaum, Mathieu; Tankov, Peter
• 署名单位: Sorbonne Universite; Universite Paris Cite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP940
• 发表日期: 2014
• 页码: 1002-1048
• 关键词: levy; errors; models

摘要

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhauser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean square discretization error for a smaller cost. We focus on discretization rules based on hitting times and give explicit expressions for the optimal rules within this class.