why does physics math apply so well in finance and biology?

double d wrote:


The mathematics of physics is well adapted to describing reasonable
smooth changes of any sort. One can liken market interactions to forces
which change the price of goods in the market place. That is a slam dunk
for the physics of classical mathematics. Think about it. We describe
prices as "movinging" up or down over time. Prices don't move in the
sense of changing locations, but change of price and change of positions
are both state changes. The math is there to describe them.

Statistical mechanics provides the math that is just right for
describing ensambles of entities. Such entities do not have to be
physical. If it could be shown that market interactions extremize
actions, even langrangians could be used.

Bob Kolker

"double d" <[Only registered users see links. ]> wrote in message
news:1117215762.128259.162520@z14g2000cwz.googlegr oups.com...

Active trading markets are, almost by definition, continuous-time
stochastic processes. A deeper result from finance, is that, to prevent
arbitrage, security prices must be (apart from some small time discounting)
martingales. Most of the time, prices move close-to-continuously and
this leads to diffusion processes.

Many of these observations were developed by Bachelier, a student of
Poincare, before Einstein's work on Brownian motion.

So, one could argue that these applications of basic probability ideas to
Wall street are quite natural and obvious. I would go farther and say that
the much
*more* surprising result is that the evolution equation for Brownian
motion,
(with a killing term added as a potential and an imaginary time rotation)
would form the basis for non-relativistic quantum mechanics. Who
would have guessed that!

This turns the question around: why does Wall Street math
(probability theory extended to imaginary time) work so well in nature? :-)

regards,
alan

Yeah, except that 3 of the 4 papers on my list rely on DISCRETE time
stochastic processes. Only Black Scholes, which you are describing,
relies on continuous time. The new trend is towards discrete time.
Md

And you're making so much of a killing in physics that, god, the worst
thing that can happen is that you can't go back?!

Your theory may explain why a new technique might penetrate wall street
and become a fad for a few weeks or months, or even years. But it
can't explain why math has survived on wall street for 35 years now
(black scholes started it in 1970). Bubbles get popped on Wall Street
under furious competition after a few years at the most. But 35 years
and still growing?

In article <d77qhk$gtc$[Only registered users see links. ].indiana.edu>,
[Only registered users see links. ] (Gregory L. Hansen) wrote:

Are you kidding? I would expect Minneapolis to be a minor seat
in financials. But why would you want to do something where
you have to wear a suit and never get dirty? oh...you'ld like
to eat.

/BAH

Subtract a hundred and four for e-mail.

Alan wrote:


I found your post interesting and informative, but I want to pick on
this one small point. Do you think that arbitraga is prevented?

Wouldn't it be more interesting to suppose that arbitrage is not
prevented, and look for arbitrage opportunities?

double d wrote:


For somebody who thinks of himself as a physicist, it's an important
thing to become an ex-physicist with an insecure future.

Someone who goes to Wall Street and lives frugally while investing
wisely might build up quite a nice early retirement even if the work
doesn't last. But it's an easier choice for physicists who can do the
work but for other reasons aren't successful with physics as a profession.

double d wrote:


Technical analysis has survived even longer. My guess is that the
evaluation process is flawed; that sometimes bad ideas that are
excellently marketed survive well. Given that, is it inevitable that
good ideas will survive?

And then *you* can lose at marketing even if the techniques are
accepted. You might do just fine for a few years marketing physicists,
and then lose out to somebody who markets ecologists to play the stock
market. It might be the same math or almost the same math, but if they
win and you lose, what good does it do you?

But of course that's true in the economy in general, not just the
market. I don't mean to suggest that the rewards don't match the risks.
Only that estate planning is much more important when you don't have
tenure.

"jonah thomas" <[Only registered users see links. ]> wrote in message
news:UwXle.4$[Only registered users see links. ]...

Thanks Jonah for your comment.

In the 'theory', an arbitrage opportunity offers the possibility
of an investment gain (with no possibility of loss)
with zero investment, i.e., an infinite return. These don't really exist.

In practice, of course, you're right in this sense:
everyone searches for investments that offer
a high ratio of, say, expected return per unit risk. The problem is that
the marketplace (say developed security markets) are filled with large
numbers
of very smart people -- the net effect is that, again, it's very difficult
to beat the 'averages'. In finance, it's called the 'efficient market
hypothesis'.
While somewhat controversial, there have been many studies establishing that
professional investors' audited results tend to be distributed in a way
consistent
with 'no unusual skill'. I spent almost 20 years at a money management firm
and you can learn that way, too, how difficult it is to beat the markets
even
if you are getting paid to do it.

But that never stops people from trying because, like the population of
Lake Wobegon, everyone with a brokerage account believes themselve to
be 'above average'. In a sense, this guarantees a virtuous circle that
keeps the efficiency going.

regards,
alan