MIMICKING MARTINGALES

• 成果类型: Article
• 署名作者: Hobson, David
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1147
• 发表日期: 2016
• 页码: 2273-2303
• 关键词: marginals; maximum; bounds

摘要

Given the univariate marginals of a real-valued, continuous-time martingale, (resp., a family of measures parameterised by t is an element of [0, T] which is increasing in convex order, or a double continuum of call prices), we construct a family of pure jump martingales which mimic that martingale (resp., are consistent with the family of measures, or call prices). As an example, we construct a fake Brownian motion. Then, under a further dispersion assumption, we construct the martingale which (within the family of martingales which are consistent with a given set of measures) has the smallest expected total variation. We also give a pathwise inequality, which in the mathematical finance context yields a model-independent sub-hedge for an exotic security with payoff equal to the total variation of the price process.