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For the past years I am thinking about relating concepts from physics to concepts from economics. Especially since the financial crisis made obvious the instability of the financial system I ask myself whether this could be explained by physics, e.g. by lack of inertia and dissipation during transactions, conservation of energy as the total amount of money available continuously increases, or whatever.

Unfortunately I am indeed not firm in physics and economics myself. However, I am yet very interested whether these ideas make any sense, or whether there is any actual research in this direction.

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closed as unclear what you're asking by dmckee Jul 10 '13 at 14:44

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i think the relevant area of expertise is called econophysics. Not sure if it deserves the name of discipline per se. –  lurscher Nov 25 '11 at 21:42
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A conservation would imply something is conserved. That something certainly isn't wealth in any real sense. Some what do you propose is conserved? –  dmckee Nov 25 '11 at 22:04

2 Answers 2

up vote 6 down vote accepted

The analogies between physics and finance are strong, so much so that the modern financial system is partly due to physicists, and mathematicians like Benoit Mandelbrot. But the applications usually come from random-walks and stochastic equations, which are related to quantum mechanics by analytic continuation in time. The ito-calculus of financial random-walks is nothing more than the Heisenberg algebra of quantum mechanics in imaginary time, where the momentum p is just $\partial_x$, without the factor of $-i$, and the commutation relation is $[x,p]=1$, without the $i$. This algebra of observables describes Brownian motion, and the short-distance structure of Brownian motion with drift, and market fluctuations, if parametrized with a time coordinate of volume traded, should ideally be a random walk or a Levy flight (walks with jumps). Further these Markovian processes need obey the Martingale property, meaning that the expected value of the asset in the future is the current value no matter how far into the future you look (compensating for the discount rate).

A random walk or Levy flight is completely stochastic and Markovian, so that each step is independent of the history. The definition of a Markovian martingale is a statement that you cannot make money by betting on stocks, just using past history as a guide. The prediction that this describes actual markets is based on efficient market hypothesis, the idea that any money that can be made has already been made, so that the remaining price fluctuations are purely Markovian. The only real evidence for the efficient market hypothesis that I see in the real world, and which is confirmed with physicist's standards of accuracy, is the hypothesis that asset prices are Markovian. If you open any newspaper and look at any price over time, you will most likely see a perfect Brownian motion.

The analog of inertia during transactions is a broker's fee, and when you can trade without a fee, there is no incentive to minimize volume, so you and a friend could swap a huge amount of a certain stock 500 times without loss, leading to fake-volume which will lead people to believe that there is a lot of trading interest in the stock. So ideal frictionless trading is a problem, and a transaction fee should incentivize against fake asset swaps of this sort, without unduly interfering with actual trades which both parties believe increase the value of their holding. I don't know the legal situation.

The recent collapse was partly due to the inability of agencies to estimate the risk of correlated loans failing simultaneously, and rating them as if they were independent. The independent risk model failed, and when property values fell below the threshhold required to make mortgage payments rational, nobody paid the mortgage, and the housing market collapsed.

There is no conservation law for wealth. The conservation law for money is violated by fractional reserve banking and central banks. The central bank is the source of money, it is amplified by fractional reserve lending at the banks, and there are several sinks, which consist of assets that drop in value, most spectacularly, a loan default. The economy just moves money from the sources to the sinks, and the rate at which it moves the money from player to player determines the income of the players.

The thermodynamic laws are not applicable here, since there is no good notion of stable equilibrium. The dynamic price equilibrium of markets is obviously a complex computing system, and not a dumb thermodynamic ensemble.

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Just a few comments (and please correct me if I'm wrong): 1) price fluctuation might not be Brownian but Geometric Brownian motion (maybe this is what you meant but did not say explicitly) 2) It is not clear they even follow Brownian motion (why Mandelbrot was pushing for something else that accounted for the heavy tails?) and 3) The stock market is not in thermodynamic equilibrium, ultimately, because the sun is dumping so much energy on us all the time... –  user834 Nov 27 '11 at 6:28
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@user834: Geometric Brownian vs. Brownian are only different for big increments, and if you look at daily fluctuations, it makes no difference which model you use, but I agree that the geometric Brownian model is better. 2. Mandelbrot sometimes wrote that they are Brownian in market time (which ticks irregularly according volume traded, not by standard time), and that the volume can have jumps which are powerlaws, leading to Levy behavior. But there are definite Brownian commodities, like wheat prices. 3. Yes, of course. –  Ron Maimon Nov 27 '11 at 8:32
    
@RonMaimon Could you give me any good reference where I can real anything else about relations and analogies between finances and physics? I enjoyed your answer (+1). –  drake Jul 31 '12 at 21:59
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@drake: Brownian derivative pricing won a Nobel in economics Black-Scholes, but the writing in the field of economics is permeated with politics. Mandelbrot is the only politics-free writer I know who deals with this. He wrote several articles on self-similar behavior in markets, and he is not an economist. "The Fractal Geometry of Nature", and "Powerlaws and 1/f noise" are both very good, but they mostly are dealing with physical systems, not economic ones. The Brownian market models are a cinch to work out compared to physics models. –  Ron Maimon Jul 31 '12 at 23:21

No, the global financial system does not violate laws of thermodynamics and energy conservation. Nothing does. These are universal laws. So, net heat will not flow from a cold bank building to its neighbouring hot bank building. An options trader cannot reach zero Kelvin. We cannot decrease the amount of entropy in the universe by moving money around.

However, the rest of your question relates to economics, not physics. It doesn't make sense to ask "if I draw this parallel between economic component X and energy, does X then behave in the same way that energy does in physics" - that' just arguing by analogy, so there's no reason why it should be true. (and it's off-topic for this site - but note StackExchange does have an economics site in beta now).

Economics and physics do share a lot of maths.

Econophysics tries to go one step further, and use concepts from physics in maths. But it is just using the same mathematical techniques though; so it's an application of some of physics' analytic tools, rather than its laws.

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