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## DETERMINISTIC FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN WHITE NOISE MODEL

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### Zulfikar Ahmed<canshoahsurvivereally@gmail.com>

4:49 PM (0 minutes ago)

 to bookprize, bookprize, chomsky, dws, hj, roberto, vlad, Jewel, Judit, Natalia, noia, Shamim, Toby, aimee

We announce the first conjectural exact science model for global volatility which is not yet worked out at all.  While fractional BROWNIAN MOTIONS are stochastic models, the FRACTIONAL DIFFERENTIAL EQUATIONS are deterministic models.  Classical signal processing had been modified already in the 1990s by David Donoho and his collaborators with their wavelet denoising technique optimal for Holder spaces and Besov spaces.  We use this technology to denoise volatility leaving Holder 0.3-0.4 ish trajectories of a deterministic fractional differential equation which we claim and hope to show in the coming weeks is an exact model for global volatility.

This step is a small step for Angel and a great step for Angelkind.

## deSolve package for ODE solutions

### Zulfikar Ahmed <wile.e.coyote.006@gmail.com>

4:18 PM (14 minutes ago)

 to David, bcc: aimee
Sir,

A simple approach to fitting fractional differential equations in code that we can use to fit a fractional differential system on a graph.  The R package deSolve does not handle fractional equations so I will do a code search since I’d rather not implement the code myself as many papers I’ve looked at give algorithms but perhaps this is a task that I can take on.  The attached paper shows an example of numerical solution of a fractional differential equation.  I did not succeed in finding code in an R or Octave package for this yet.
Possible task:  implement direct modeling for solving and simulating deterministic fractional differential equations.  This is a concrete task that will allow us to explore the exact models for volatility dynamics we hope.

Attachments area
Preview attachment 2010 Physics Letters, Section A, General, Atomic and Solid State Physics 374(25).pdf

2010 Physics Letters, Section A, General, Atomic and Solid State Physics 374(25).pdf

### Zulfikar Ahmed <wile.e.coyote.006@gmail.com>

4:33 PM (0 minutes ago)

 to David
An example makes the ‘variation iteration method’ pretty clear.  One needs at each step the ability to be able to calculate the appropriate fractional derivatives.  Now fractional derivatives and their generalizations can be coded directly from a numerical integration whether we take one of the several variations for the definition of fractional derivative defined by

(d/dt)^alpha u(t) = const \int_0^t (t-s)^{alpha-1} u(s)ds
in R for example:

fracdiff<-function( u, alpha, t0){

# t0=index
c<-1/gamma(alpha)
v<-0
for (i in 1:t0){
v<-v+pow(abs(float(i)-t0)),alpha-1)*u[i]
}
v
}
Now the iterative method is simply updating solutions with updates which involve this fractional derivative and other terms in the equation.  These have good convergence properties.
Now we’re interested in actually using data to estimate the fractional differential equation that will be the first law of volatility say, so we fix the Hurst parameter (giving us exact value for alpha) and we estimate F(u) using the linear model we’ve begun with.  So then we’re almost to a law for volatility without any idea of how it will fit.
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4:49 PM (0 minutes ago)

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From: Zulfikar Ahmed <canshoahsurvivereally@gmail.com>
To: bookprize@harvardclubsf.com, bookprize@harvardclubsf.org, chomsky@mit.edu, dws@mit.edu, hj@falconfone.con, roberto@gwu.edu, vlad@glassbeadcollective.org, Jewel Hasan <jewel.hasan@gmail.com>, Judit Revesz <judit.revesz@gmail.com>, Natalia Brizuela <nbrizuela@gmail.com>, noia efrat <noia.efrat@gmail.com>, Shamim Sadiq <ssadiq@praxisfinancial.com>, Toby Ferooz <fertobah@gmail.com>, aimee lund <namewithdrawn@gmail.com>
Cc:
Date: Thu, 11 Jun 2015 16:49:38 -0700
Subject: DETERMINISTIC FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN WHITE NOISE MODEL

We announce the first conjectural exact science model for global volatility which is not yet worked out at all.  While fractional BROWNIAN MOTIONS are stochastic models, the FRACTIONAL DIFFERENTIAL EQUATIONS are deterministic models.  Classical signal processing had been modified already in the 1990s by David Donoho and his collaborators with their wavelet denoising technique optimal for Holder spaces and Besov spaces.  We use this technology to denoise volatility leaving Holder 0.3-0.4 ish trajectories of a deterministic fractional differential equation which we claim and hope to show in the coming weeks is an exact model for global volatility.

This step is a small step for Angel and a great step for Angelkind.

## deSolve package for ODE solutions

### Zulfikar Ahmed <wile.e.coyote.006@gmail.com>

4:18 PM (14 minutes ago)

 to David, bcc: aimee
Sir,

A simple approach to fitting fractional differential equations in code that we can use to fit a fractional differential system on a graph.  The R package deSolve does not handle fractional equations so I will do a code search since I’d rather not implement the code myself as many papers I’ve looked at give algorithms but perhaps this is a task that I can take on.  The attached paper shows an example of numerical solution of a fractional differential equation.  I did not succeed in finding code in an R or Octave package for this yet.
Possible task:  implement direct modeling for solving and simulating deterministic fractional differential equations.  This is a concrete task that will allow us to explore the exact models for volatility dynamics we hope.

Attachments area
Preview attachment 2010 Physics Letters, Section A, General, Atomic and Solid State Physics 374(25).pdf

2010 Physics Letters, Section A, General, Atomic and Solid State Physics 374(25).pdf

### Zulfikar Ahmed <wile.e.coyote.006@gmail.com>

4:33 PM (0 minutes ago)

 to David
An example makes the ‘variation iteration method’ pretty clear.  One needs at each step the ability to be able to calculate the appropriate fractional derivatives.  Now fractional derivatives and their generalizations can be coded directly from a numerical integration whether we take one of the several variations for the definition of fractional derivative defined by

(d/dt)^alpha u(t) = const \int_0^t (t-s)^{alpha-1} u(s)ds
in R for example:

fracdiff<-function( u, alpha, t0){

# t0=index
c<-1/gamma(alpha)
v<-0
for (i in 1:t0){
v<-v+pow(abs(float(i)-t0)),alpha-1)*u[i]
}
v
}
Now the iterative method is simply updating solutions with updates which involve this fractional derivative and other terms in the equation.  These have good convergence properties.
Now we’re interested in actually using data to estimate the fractional differential equation that will be the first law of volatility say, so we fix the Hurst parameter (giving us exact value for alpha) and we estimate F(u) using the linear model we’ve begun with.  So then we’re almost to a law for volatility without any idea of how it will fit.