Re: fuzzy finance


Subject: Re: fuzzy finance
From: Will Dwinnell (predictor@compuserve.com)
Date: Wed Mar 01 2000 - 16:09:21 MET


Paul Victor Birke wrote:
"There is a Fuzzy Price! The price quoted is only one of a possible number from a small
interval set. Usually a Uniform Distribution defined by {PriceLOW, PriceHIGH} also
there is another way using a sort of Trapezoid FF with {PriceULTRALOW, PriceLOW,
PriceMEAN, PriceHIGH,PriceULTRAHIGH}. The Ultra values define the Trapezoid boundaries
having zero membership value. The Low and High define the limits of the membership = 1
Uniform Distribution. The Mean may or may not be in the centre between Low and High."

Will Dwinnell wrote:
"Is that a fuzzy price or a probabilistic one? It sounds like you are describing a
probability distribution."

Paul Victor Birke responded:
"Well I think this is a good point. Admittedly, it could look like a PDF.

However, I think it depends where you are coming from-what formulates your analysis
context. I tend to think markets and prices are best viewed as fuzzy. In fact, I think
many markets can be modelled via an UltraFuzzy Function. This analysis context seems
more natural to me. I don't know if there is a counterpart in Probability Theory to the
concept of an UltraFuzzy Function although one could certainly have lower and upper
PDFs.

Here, we are trying to place a price in the context of a membership formulation. I
think the Uniform Distribution part speaks to this. We are saying the membership is 1.0
for a finite range and falls off on either side. You can use this for sure, that is,
membership = 1.0 here in this interval. The membership value falls away to zero on
either side and this can be asymmetric as PUL and PUH could be anywhere.

Would be interested to hear you views?"

I was just thinking that, in the end, a buyer pays only a single price. Certainly,
before the transaction, available information may allow us to infer some distribution of
price values, but both probability and fuzzy logic deal in distributions. Once the
transaction has occurred, however, the price is known, which makes this seem more like a
probability issue to me.

Will Dwinnell
predictor@compuserve.com

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