On the properties of r-excessive mappings for a class of diffusions

• 成果类型: Article
• 署名作者: Alvarez, LHR
• 署名单位: University of Turku
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1069786509
• 发表日期: 2003
• 页码: 1517-1533
• 关键词: uncertainty

摘要

We consider the convexity and comparative static properties of a class of r-harmonic mappings for a given linear, time-homogeneous and regular diffusion process. We present a set of weak conditions under which the minimal r-excessive mappings for the considered diffusion are convex and under which an arbitrary nontrivial r-excessive mapping is convex on the regions where it is r-harmonic. Consequently, we are able to present a set of usually satisfied, conditions under which increased volatility increases the value of r-harmonic mappings. We apply our results to a class of optimal stopping problems arising frequently in studies considering the pricing of perpetual American contingent claims and state a set of conditions under which the value function is convex on the continuation region and, consequently, under which increased volatility unambiguously increases the value function and expands the continuation region, thus postponing the rational exercise of the claim.