WEAK TAIL CONDITIONS FOR LOCAL MARTINGALES

• 成果类型: Article
• 署名作者: Hulley, Hardy; Ruf, Johannes
• 署名单位: University of Technology Sydney; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1302
• 发表日期: 2019
• 页码: 1811-1825
• 关键词: ASSET PRICE BUBBLES; uniform integrability; QUADRATIC VARIATION; criterion; options

摘要

The following conditions are necessary and jointly sufficient for an arbitrary cadlag local martingale to be a uniformly integrable martingale: (A) The weak tail of the supremum of its modulus is zero; (B) its jumps at the first-exit times from compact intervals converge to zero in L-1 on the events that those times are finite; and (C) its almost sure limit is an integrable random variable.