Analysis of continuous strict local martingales via h-transforms

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Pal, Soumik²  Protter, Philip¹ 

[1] Cornell Univ, ORIE, Ithaca, NY 14853 USA

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

关键词: Local martingale;    Strict local martingale;    Inverse Bessel process;    Financial bubble;   

DOI  :  10.1016/j.spa.2010.04.004

来源: Elsevier

【 摘 要 】

We study strict local martingales via h-transforms, a method which first appeared in work by Delbaen and Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are identified. We treat examples of diffusions with various boundary behavior, size-bias sampling of diffusion paths, and non-colliding diffusions. A multidimensional generalization to conformal strict local martingales is achieved through Kelvin transform. As curious examples of nonstandard behavior, we show by various examples that strict local martingales do not behave uniformly when the function (x - K)(+) is applied to them. Implications to the recent literature on financial bubbles are discussed. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free