A CLARK-OCONE FORMULA FOR TEMPORAL POINT PROCESSES AND APPLICATIONS

• 成果类型: Article
• 署名作者: Flint, Ian; Torrisi, Giovanni Luca
• 署名单位: Nanyang Technological University; Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1136
• 发表日期: 2017
• 页码: 3266-3292
• 关键词: variational representation; conditional intensity; approximation; functionals

摘要

We provide a Clark-Ocone formula for square-integrable functionals of a general temporal point process satisfying only a mild moment condition, generalizing known results on the Poisson space. Some classical applications are given, namely a deviation bound and the construction of a hedging portfolio in a pure-jump market model. As a more modern application, we provide a bound on the total variation distance between two temporal point processes, improving in some sense a recent result in this direction.