Analysis of continuous strict local martingales via h-transforms

作者：Pal Soumik; Protter Philip^*

来源：Stochastic Processes and Their Applications, 2010, 120(8): 1424-1443.

DOI：10.1016/j.spa.2010.04.004

• Local martingale
• Strict local martingale
• Inverse Bessel process
• Financial bubble

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 x - K)(+) is applied to them. Implications to the recent literature on financial bubbles are discussed.

• 出版日期2010-8