Re: fuzzy finance


Subject: Re: fuzzy finance
From: Paul Victor Birke (nonlinear@home.com)
Date: Wed Mar 01 2000 - 13:34:14 MET


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

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?

Paul

############################################################################
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3) To reach the human who maintains the list, send mail to
fuzzy-owner@dbai.tuwien.ac.at
(4) WWW access and other information on Fuzzy Sets and Logic see
http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html



This archive was generated by hypermail 2b25 : Thu Apr 06 2000 - 15:59:46 MET DST