Analysis of continuous strict local martingales via h-transforms
By Soumik Pal, Philip Protter. 2007
76 citations recorded by the source corpus.
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 non-standard 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.
Subfields: Economics and Econometrics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/719a3bc230896ed15659e1e8547dd8cb70772303
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
- Aleksandar Mijatovic
- Philip Protter
- Mikhail Urusov
- Hans Föllmer
- Alexander Schied
- Andrzej Ruszczynski
- Alexander Shapiro
- Andreas Tsanakas
In Finance
- Philip Protter
- Hans Föllmer
- Aleksandar Mijatovic
- Mikhail Urusov
- Alexander Schied
- Andrzej Ruszczynski
- Alexander Shapiro
- Jan Kallsen
In Mathematical Physics
Citations in the corpus
- Local martingales and filtration shrinkage (2011, background): “Much is known about the inverse Bessel process, and one can consult (as one example among many) the recent article [25] or the classic text [28].”
- HEDGING UNDER ARBITRAGE (2010, unknown): “ForS(0) = 1, simple computations will lead directly to Equation (6) of Pal and Protter (2010).”
- On the martingale property of certain local martingales (2009, background): “Bubbles have recently attracted attention in the mathematical finance literature; see e.g. Cox and Hobson [9], Ekström and Tysk [13], Heston, Loewenstein, and Willard [19], Jarrow, Protter, and Shimbo [22], Madan and Yor [32], Pal and Protter [36].”