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Collector
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Re: negative transition probability

November 12th, 2016, 2:00 pm

Have  a good flight. I hope the person sitting next to you does not report you to the FBI. Under no circumstances, write anything down.
The main issue is these NegProbs have no +, *,_.
the good thing with such a side job is free parking almost anywhere, the boring part is all the emails one has to skim through, mostly about yoga pants. Hardly any time for investigating negative probabilities. (most academics need a side job to make the ends meet, why not one with free parking almost anywhere) 
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Last edited by Collector on November 12th, 2016, 2:03 pm, edited 1 time in total.
 
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Traden4Alpha
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Re: negative transition probability

November 12th, 2016, 2:02 pm

The mathematical properties for 'extended probability' seem well defined in section 2 of B/M.  What other "mathematical foundations" do you need?

And implementing negative probabilities to the binomial method for interest rates implies definining how rates might transition from a positive rate to a negattive rate (or back) with the mass of negative rate states being members of the anti-event set which offsets respective positive rate events.  I'm sure the people that study the evolution of market rates have some sense of this diffusion or jump process.

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.
 
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Cuchulainn
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Re: negative transition probability

November 12th, 2016, 3:37 pm

The mathematical properties for 'extended probability' seem well defined in section 2 of B/M.  What other "mathematical foundations" do you need?

As I wrote in my previous posts. I am not going to repeat them. Or look at Feynman's good examples.
A bunch of axioms is not enough.
I think we are separated by a common language (English and linguistics) while it should be the languages of mathematics.

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.

Now you're talkin' It is called a model error. But binomial can break down even for good models, a (math) defect.
 
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Collector
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Re: negative transition probability

November 12th, 2016, 4:04 pm

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.

Now you're talkin' It is called a model error. But binomial can break down even for good models, a (math) defect.
CRR yes, not Rendleman–Bartter?, or would you say both ("any" binomial )? 

and all these models are also based on series of hidden assumptions that yes tend to break down totally now and then, likely series of interesting topics here for discussion and developments in extended probabilities.
 
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Cuchulainn
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Re: negative transition probability

November 13th, 2016, 9:52 pm

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.

Now you're talkin' It is called a model error. But binomial can break down even for good models, a (math) defect.
CRR yes, not Rendleman–Bartter?, or would you say both ("any" binomial )? 

and all these models are also based on series of hidden assumptions that yes tend to break down totally now and then, likely series of interesting topics here for discussion and developments in extended probabilities.
"All models are wrong, some are useful".
All hidden assumptions must be flagged and made explicit. The need to concoct negative probabilities is due to the model and/or binomial approximation to it.
A real example is the BDT model for humped IR curves in combination with Newton Raphson crashe for some values of the volatility > 60%. Why is that?
 
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Cuchulainn
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Re: negative transition probability

November 13th, 2016, 9:52 pm

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.

Now you're talkin' It is called a model error. But binomial can break down even for good models, a (math) defect.
CRR yes, not Rendleman–Bartter?, or would you say both ("any" binomial )? 

and all these models are also based on series of hidden assumptions that yes tend to break down totally now and then, likely series of interesting topics here for discussion and developments in extended probabilities.
"All models are wrong, some are useful".
All hidden assumptions must be flagged and made explicit. The need to concoct negative probabilities is due to the model and/or binomial approximation to it.
A real example is the BDT model for humped IR curves in combination with Newton Raphson crashes for some values of the volatility > 60%. Why is that? Answer; The holy example of yield == 5% as seed is wrong. First bracket the solution and then NR.
 
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Traden4Alpha
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Re: negative transition probability

November 14th, 2016, 1:21 pm

The mathematical properties for 'extended probability' seem well defined in section 2 of B/M.  What other "mathematical foundations" do you need?

As I wrote in my previous posts. I am not going to repeat them. Or look at Feynman's good examples.
A bunch of axioms is not enough.
I think we are separated by a common language (English and linguistics) while it should be the languages of mathematics.

Of course, if we just get rid of the silly log model that requires prices or rates to be positive, then we could dispense with the need for negative 'extended probability' in order fit empirically true scenarios into this unrealistic math model.

Now you're talkin' It is called a model error. But binomial can break down even for good models, a (math) defect.
Yes, language is an issue.  Yet math is interesting in its abilities to construct new, alternatives such as different probability measures, algebras, etc.  It's then a matter of language to decide whether each alternative has a unique name or uses a shared name with specific properties in each specific context (i.e., the namespace concept in software).
Yes, it's model error but, in fairness, i-rates seem hard to model in the curious assymetry of the tails of their distribute.  Zero is not the hard limit that it seems to be.
 
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Cuchulainn
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Re: negative transition probability

November 14th, 2016, 5:49 pm

Yes, it's model error but, in fairness, i-rates seem hard to model in the curious assymetry of the tails of their distribute.  Zero is not the hard limit that it seems to be.

Indeed, a bell-shaped/humped  curve in which mid-term rates are higher than either of short-term and long-terms rates. It is rare and a sign of economic downturn. Down the chain, the usual numerical methods can fail.

I suppose root-cause analysis is advised.
 
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Collector
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Re: negative transition probability

November 14th, 2016, 6:50 pm

All hidden assumptions must be flagged and made explicit. 
This is over optimistic even for honest applied mathematicians. The problem is one has often not even thought about (or enough knowledge about) all the assumptions that then should to stated. At least if it is going to be used for something applied outside pure mathematics.

Good applied mathematics and probability theory must ultimately be rooted in good physics. And also other way around, but if part of  the depth of reality is discrete then for example probabilities based on continuous mathematics will fail in the limit?
 
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Cuchulainn
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Re: negative transition probability

November 14th, 2016, 7:21 pm

All hidden assumptions must be flagged and made explicit. 
This is over optimistic even for honest applied mathematicians. The problem is one has often not even thought about (or enough knowledge about) all the assumptions that then should to stated. At least if it is going to be used for something applied outside pure mathematics.

Good applied mathematics and probability theory must ultimately be rooted in good physics. And also other way around, but if part of  the depth of reality is discrete then for example probabilities based on continuous mathematics will fail in the limit?
The Scientific Method might be useful here
https://www.youtube.com/watch?v=EYPapE-3FRw
 
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Cuchulainn
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Re: negative transition probability

November 14th, 2016, 7:53 pm

Good applied mathematics and probability theory must ultimately be rooted in good physics.
??
Physics is neither sufficient nor necessary for mathematics. Most physics theories are not even wrong.
 
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Collector
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Re: negative transition probability

November 14th, 2016, 8:06 pm

All hidden assumptions must be flagged and made explicit. 
This is over optimistic even for honest applied mathematicians. The problem is one has often not even thought about (or enough knowledge about) all the assumptions that then should to stated. At least if it is going to be used for something applied outside pure mathematics.

Good applied mathematics and probability theory must ultimately be rooted in good physics. And also other way around, but if part of  the depth of reality is discrete then for example probabilities based on continuous mathematics will fail in the limit?
The Scientific Method might be useful here
https://www.youtube.com/watch?v=EYPapE-3FRw
One of the main problems is experiments often are ignored for decades. Early 1900 series of empirical research showed returns in commodity prices and stocks where far from normal distributed. This was for example ignored by people like Osborne who even himself found the same in his empirical data in 1959, but claimed the data where wrong and the Gaussian model (GBM) had to be correct.

Exactly same happened in studies of galaxy velocity distributions even 1990´s, the observations was ignored as incorrect data for many years before one admitted data correct, model wrong. Actually such loosely scientific attitude in astronomy (ignoring the data) was pointed out by swedish mathematician already early 1900. 

We unfortunately see the same in other scientific disciplines even to this date, observations and experiments (that even are relatively cheaply to repeat) are simply ignored if not fit main frame model framework. Instead we often see the model more and more wrapped in with complex math and multiple layers of buzz words.

this is totally against the scientific method outlined by Feyman.

series of scientist have invested too many years in building bubble models to even admit thy ignore observations. 
 
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Collector
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Re: negative transition probability

March 10th, 2017, 11:06 pm

An Introduction to Symmetric Inflated Probabilities by Mark Burgin  (2017)

"Some even assert that probabilities that can be negative, larger than 1 or less than −1 are necessary for physics. Here we develop an axiomatic system for such probabilities, which are called symmetric inflated probabilities and reflect interaction of particles and antiparticles, and study their properties."
 
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Cuchulainn
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Re: negative transition probability

March 11th, 2017, 10:48 am

"What's in a name? That which we call a rose
By any other name would smell as sweet."
 
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Collector
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Re: negative transition probability

May 21st, 2017, 9:18 pm

Microsoft Research;  https://www.microsoft.com/en-us/researc ... 01/224.pdf

Could it be that there are some wrong assumptions in physics somewhere that currently are ''fixed" with negative quasi probabilities?