scholarly journals Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models

2010 ◽  
Vol 16 (2) ◽  
pp. 225-247 ◽  
Author(s):  
Aleksandar Mijatović ◽  
Mikhail Urusov
2015 ◽  
Vol 46 (9) ◽  
pp. 983-995 ◽  
Author(s):  
J. E. de Farias Aires ◽  
A. F. da Silva Júnior ◽  
K. L. C. de Almeida Farias Aires ◽  
V. S. de Oliveira Farias ◽  
C. M. D. P. da Silva e Silva ◽  
...  

2021 ◽  
Vol 25 (2) ◽  
pp. 359-381
Author(s):  
Sascha Desmettre ◽  
Gunther Leobacher ◽  
L. C. G. Rogers

AbstractIt is generally understood that a given one-dimensional diffusion may be transformed by a Cameron–Martin–Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this, we have to know that the change-of-measure local martingale that we write down is a true martingale. We provide a complete characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.


1983 ◽  
Vol 93 (7) ◽  
pp. 349-350 ◽  
Author(s):  
Robert Kariotis ◽  
Michael J. Stephen

2021 ◽  
Vol 22 (5) ◽  
pp. 2398
Author(s):  
Wooyoung Kang ◽  
Seungha Hwang ◽  
Jin Young Kang ◽  
Changwon Kang ◽  
Sungchul Hohng

Two different molecular mechanisms, sliding and hopping, are employed by DNA-binding proteins for their one-dimensional facilitated diffusion on nonspecific DNA regions until reaching their specific target sequences. While it has been controversial whether RNA polymerases (RNAPs) use one-dimensional diffusion in targeting their promoters for transcription initiation, two recent single-molecule studies discovered that post-terminational RNAPs use one-dimensional diffusion for their reinitiation on the same DNA molecules. Escherichia coli RNAP, after synthesizing and releasing product RNA at intrinsic termination, mostly remains bound on DNA and diffuses in both forward and backward directions for recycling, which facilitates reinitiation on nearby promoters. However, it has remained unsolved which mechanism of one-dimensional diffusion is employed by recycling RNAP between termination and reinitiation. Single-molecule fluorescence measurements in this study reveal that post-terminational RNAPs undergo hopping diffusion during recycling on DNA, as their one-dimensional diffusion coefficients increase with rising salt concentrations. We additionally find that reinitiation can occur on promoters positioned in sense and antisense orientations with comparable efficiencies, so reinitiation efficiency depends primarily on distance rather than direction of recycling diffusion. This additional finding confirms that orientation change or flipping of RNAP with respect to DNA efficiently occurs as expected from hopping diffusion.


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