AFFINE PROCESSES BEYOND STOCHASTIC CONTINUITY

• 成果类型: Article
• 署名作者: Keller-Ressel, Martin; Schmidt, Thorsten; Wardenga, Robert
• 署名单位: Technische Universitat Dresden; University of Freiburg; University of Freiburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1483
• 发表日期: 2019
• 页码: 3387-3437
• 关键词: term structure; Dividend policy

摘要

In this paper, we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting, times of jumps can be both inaccessible and predictable. To this end, we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equations of Riccati type. We prove existence of affine Markov processes and affine semimartingales under mild conditions and elaborate on examples and applications including affine processes in discrete time.