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Theoretical Foundation for the Inverse Power Law Distribution

Victor Aguilar

posted on 20 December 2013

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It has come to my attention that a solution to the puzzle of why large fluctuations in prices have an inverse power law distribution goes unanswered.  This is an easy corollary to the principal result of my 1999 book, Axiomatic Theory of Economics, Theorem 12, the Law of Price Adjustment, summarized in this paper.

 

My theory describes a single instant in time.  Of course, instants have the habit of following one another, eventually forming something called history.  So it is natural to inquire, not just what the price is at a given instant, but what the distribution of price changes is over history.  This I did not do in 1999.

 

Addressing this issue requires an additional axiom: the parameter called importance, μ, must have an exponential distribution, λe-λμ.  Specifically, the inverse cubic law requires that the underlying distribution be 2e-2μ.

 

In point of fact, the only restriction that I placed on μ is that it be a non-negative real number.  But negative monotonic distributions with this support and moments of all orders are not that numerous.  Why not the exponential?  The fact that an exponential distribution of μ implies an inverse power law distribution of large price fluctuations is motivation enough for most economists to accept this new axiom, and my other results require only that the distribution of μ be negative monotonic on [0,∞).

Discussion

Brian Lucey’s creative editing

 

I submitted this paper to the International Review of Financial Analysis.  Editor Brian Lucey rejected my paper on the basis of pulling a phrase out of the middle of a sentence and capitalizing the first word to make it look like he was quoting a complete sentence.  How clever!

 

Here I quote Mr. Lucey verbatim with his own comments in square brackets, just as they appeared in his rejection letter, and displaying his characteristic style of writing questions without question marks:

 

“People never need more than one of anything at a time. [What does this mean.  There are many counter examples, especially investments.]”

 

Here I quote the passage in full:

 

“Most of the real analysis in Axiomatic Theory of Economics stems from the infinite summation, c(m).  To simplify the proofs in this article, the second axiom is replaced with the assertion that people never need more than one of anything at a time.  This assumption is neither accurate nor necessary, as all of the results of my theory can be (and are) proven in their full generality.  However, some economists do not have the mathematical background necessary to read Axiomatic Theory of Economics, so, for expository purposes, simplified proofs are provided here.”

 

It is amazing what a little creative editing can do!

 

In point of fact, my second axiom reads: 

 

“Diminishing utility is independent of first-unit demand, it is negative monotonic, and the integral from zero to infinity is finite.”

Brian Lucey smears me by pulling a phrase out of the middle of a sentence and capitalizing the first word to make it look like he was quoting a complete sentence.  But my paper has now been downloaded over 500 times, which proves that there are many people who wish to judge me based on what I actually wrote, not on the edited version that Brain Lucey is peddling.

 

How many copies of the special econophysics edition to the International Review of Financial Analysis has Brain Lucey sold in this time?  None.  He pocketed my $150 submission fee and then canceled the project after launching his smear campaign against me.  Thief!