Financial mathematics and Nonlocal electrostatics: Difference between pages

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Nonlocal equations are common in financial mathematics because the prices of assets can be modeled following any [[Levy processes|Levy process]]. In particular jump processes are natural since asset prices can have a sudden change.
Nonlocal electrostatics is a technique currently under development which may turn into a powerfull tool for drug design <ref name="ICH"/> <ref name="HBRK"/> <ref name="SBRF"/>.


The Black–Scholes model, which is used to price derivatives, is essentially a parabolic integro-differential equation for European options, and an [[obstacle problem]] for American options.
The idea is that when computing the electric potential around a protein, which is surrounded by water, this potential interacts with the ions in the water, which affect the potential effectively transforming it from the classical coulomb potential (i.e. the fundamental solution of the Laplacian) to the potential of an integral operator (the fractional Laplacian in the simplest case). Experimentally, this has shown to provide a much more accurate model to predict protein docking (if two proteins will stuck together). When seeking drug which would interact with certain protein, the first step is to look for molecule which will stick to the desired protein, and that is when this methods become very useful.


A good reference for financial modeling with jump processes is the book of Rama Cont and Peter Tankov <ref name="CT"/>
== Links ==
There is a group in the center for Bioinformatics in Saarland University doing research in this field actively. They have a webside describing the project
http://bioinf-www.bioinf.uni-sb.de/projects/solvation


==Refences==
== References ==
{{reflist|refs=
{{reflist|refs=
<ref name="CT">{{Citation | last1=Cont | first1=Rama | last2=Tankov | first2=Peter | title=Financial modelling with jump processes | publisher=Chapman & Hall/CRC, Boca Raton, FL | series=Chapman & Hall/CRC Financial Mathematics Series | isbn=978-1-58488-413-2 | year=2004}}</ref>
<ref name="ICH">{{Citation | last1=Ishizuka | first1=R | last2=Chong | first2=S-H | last3=Hirata | first3=F | title=An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach. | url=http://www.ncbi.nlm.nih.gov/pubmed/18205507 | publisher=AIP | year=2008 | journal=The Journal of Chemical Physics | volume=128 | issue=3 | pages=034504}}</ref>
<ref name="HBRK">{{Citation | last1=Hildebrandt | first1=A. | last2=Blossey | first2=R. | last3=Rjasanow | first3=S. | last4=Kohlbacher | first4=O. | last5=Lenhof | first5=H.P. | title=Electrostatic potentials of proteins in water: a structured continuum approach | publisher=Oxford Univ Press | year=2007 | journal=Bioinformatics | volume=23 | issue=2 | pages=e99}}</ref>
<ref name="SBRF">{{Citation | last1=Scott | first1=R. | last2=Boland | first2=M. | last3=Rogale | first3=K. | last4=Fernández | first4=A. | title=Continuum equations for dielectric response to macro-molecular assemblies at the nano scale | publisher=IOP Publishing | year=2004}}</ref>
}}
}}
{{stub}}

Revision as of 19:04, 6 July 2011

Nonlocal electrostatics is a technique currently under development which may turn into a powerfull tool for drug design [1] [2] [3].

The idea is that when computing the electric potential around a protein, which is surrounded by water, this potential interacts with the ions in the water, which affect the potential effectively transforming it from the classical coulomb potential (i.e. the fundamental solution of the Laplacian) to the potential of an integral operator (the fractional Laplacian in the simplest case). Experimentally, this has shown to provide a much more accurate model to predict protein docking (if two proteins will stuck together). When seeking drug which would interact with certain protein, the first step is to look for molecule which will stick to the desired protein, and that is when this methods become very useful.

Links

There is a group in the center for Bioinformatics in Saarland University doing research in this field actively. They have a webside describing the project http://bioinf-www.bioinf.uni-sb.de/projects/solvation

References

  1. Ishizuka, R; Chong, S-H; Hirata, F (2008), "An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach.", The Journal of Chemical Physics (AIP) 128 (3): 034504, http://www.ncbi.nlm.nih.gov/pubmed/18205507 
  2. Hildebrandt, A.; Blossey, R.; Rjasanow, S.; Kohlbacher, O.; Lenhof, H.P. (2007), "Electrostatic potentials of proteins in water: a structured continuum approach", Bioinformatics (Oxford Univ Press) 23 (2): e99 
  3. Scott, R.; Boland, M.; Rogale, K.; Fernández, A. (2004), Continuum equations for dielectric response to macro-molecular assemblies at the nano scale, IOP Publishing