Minimal fq-martingale measures for exponential levy processes

• 成果类型: Article
• 署名作者: Jeanblanc, Monique; Kloeppel, Susanne; Miyahara, Yoshio
• 署名单位: Universite Paris Saclay; Nagoya City University; Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP439
• 发表日期: 2007
• 页码: 1615-1638
• 关键词: martingale measures; Optimal portfolios

摘要

Let L be a multidimensional Levy process under P in its own filtration. The p-minimal martingale measure Q(q) is defined as that equivalent local martingale measure for 8 (L) which minimizes the f(q)-divergence E[(dQ/dp)(q)] for fixed q epsilon (-infinity, 0) boolean OR (1, infinity). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q = 2, we relate the sufficient conditions to the structure condition and discuss when the former are also necessary. Moreover, we show that Qq converges for q SE arrow 1 in entropy to the minimal entropy martingale measure.