QuoteOriginally posted by: NYes, but the dynamics of those air or water molecules are neither plain or well understood, and one of Einstein's few major mistakes was his PhD paper on Browning motion. You see the Navier-Stokes PDE that governs the mass transport problem (Brownian motion) is still an open problem in mathematical-physics.I'd say you're a victim of 'folk' math.Let me clarify - the Navier-Stokes equation deals with momentum transport, not mass. The convection-diffusion equation is the mass transfer equation. Alternatively, you have the heat equation, which is identical to the convection-diffusion equation, but with temperature, instead of concentration, being the dependent variable.The Navier Stokes is not an open problem. It is the general PDE (based on Newton's F= dp/dt) that describes the dynamics of incompressible viscous flow. Its solution depends on initial and boundary conditions and getting these solutions, mainly in closed form or even numerically, is where the challenges lie. The same story applies to the diffusion equation, which is based on brownian motion. The equation is well understood and is there for everyone to use, but solving it for different BCs and ICs presents the major challenge, as, I'm sure, Cuchulainn can testify. When you solve it, you're not concerned with whether or not brownian motion is plain or exotic, you just want to solve it. As a result, when it comes to solving any of these equations, the molecular dynamics, along with brownian motion, no matter how complicated they may be, lie in the background and you don't even want to think about them.These are not "folk" math and there's nothing exotic about them either. They represent the foundation of fluid mechanics and heat and mass transfer and as a sophomore they get hammered into your head. Come on! Do I have to tell you all this??

QuoteThe same story applies to the diffusion equation, which is based on brownian motion. The equation is well understood and is there for everyone to use, but solving it for different BCs and ICs presents the major challenge, as, I'm sure, Cuchulainn can testify. When you solve it, you're not concerned with whether or not brownian motion is plain or exotic, you just want to solve it. As a result, when it comes to solving any of these equations, the molecular dynamics, along with brownian motion, no matter how complicated they may be, lie in the background and you don't even want to think about them.I agree with you Ruben. What I have seen in many posts is that they quickly become polluted with nonsensical discussions. Take this post, for example. It will go the way of the 'sigma algebra' post. Well done N.

Thanks for all your ideas. With regards to my talk there is certainly lots of good stuff that I can take from this. Actually, as I only have an hour I'll have to be very picky, and likely won't make it on to anything particularly complex. I'll have to motivate the talk by asserting what I may like to find out / calculate; the majority of the audience will question how I intend to predict future stock prices, so I'll have to steer towards some simple hedging example. One of my peers thinks banks are awful because of his experience of Lloyds TSB. So, obviously I've got my work cut out trying to win over the the die hard anti finance guys. Still, I'm certain that there is a lot of interesting maths that my peers should be interested in; I hope they are willing to see it applied to something unfamiliar.At this point I will aim to derive BS, no doubt motivated by some discussion of 'plain old brownian motion'. I'm perhaps not in a position to question whether it is plain or old, but I think the views expressed here are probably useful. Certainly it seems that my elementary talk could be constructed on well defined / well understood ground. In all honesty I've yet to calculate anything particularly exotic, in a way that cannot be expressed in simple brownian motion terms, so it's unlikely I'll extend my talk into unsure territory. So, perhaps I'll get as far as pricing a simple option, motivated using some risk management example. Possibly by this point I'll have lost some people. So, I'd like to give an example of how a technique used in our group may be used in finance. Specifically I'd like to try to find a simple application of a genetic algorithm. I've had a look around the forum, but I've not found a good, simple example as yet. Ideally it would be of the form: Here's some parameter space to search. If I find the answer it's good. Ok, so that's very vague. My point is I don't want to talk about using the algorithm to calibrate a model; it's too complex. Any ideas would be great, though I'm happy to keep trawling. Thankyou for all your contibutions!Hens

QuoteOriginally posted by: CuchulainnQuoteThe same story applies to the diffusion equation, which is based on brownian motion. The equation is well understood and is there for everyone to use, but solving it for different BCs and ICs presents the major challenge, as, I'm sure, Cuchulainn can testify. When you solve it, you're not concerned with whether or not brownian motion is plain or exotic, you just want to solve it. As a result, when it comes to solving any of these equations, the molecular dynamics, along with brownian motion, no matter how complicated they may be, lie in the background and you don't even want to think about them.I agree with you Ruben. What I have seen in many posts is that they quickly become polluted with nonsensical discussions. Take this post, for example. It will go the way of the 'sigma algebra' post. Well done N.Actually Cuch, I'm quite amazed that you and cohen have no clue regarding solutions of irreducible 2nd order PDEs (eg convection-diffusion). Don't you remember Fermi, Pasta and Ulam (ULM) experiments from the early '50s where they blew apart statistical mechanics theory because the energy didn't distribute as expected into the normal modes? Applied mathematics hasn't been the same since - including major discoveries by Lax and others.Sigma algebras require the second counting axiom (aka Axioim of Choice). No credible mathematician depends on AC or uses sigma algebras."Well done"... Thanks, just doing my part to remove 'junk' math from finance.

QuoteOriginally posted by: NActually Cuch, I'm quite amazed that you and cohen have no clue regarding solutions of irreducible 2nd order PDEs (eg convection-diffusion). Don't you remember Fermi, Pasta and Ulam (ULM) experiments from the early '50s where they blew apart statistical mechanics theory because the energy didn't distribute as expected into the normal modes? Applied mathematics hasn't been the same since - including major discoveries by Lax and others.Sigma algebras require the second counting axiom (aka Axioim of Choice). No credible mathematician depends on AC or uses sigma algebras."Well done"... Thanks, just doing my part to remove 'junk' math from finance.N,This needs to be straightened out - the equations (Navier-Stokes, Diffusion and Heat) are "continuous", not statistical. Navier-Stokes applies Newton's 2nd law of motion to incompressible and viscous fluids, Diffusion utilizes brownian motion as its foundation and Heat is based on the laws of conduction (Fourier) and cooling (Newton). The derivation of all of these is based on continuum assumptions. I don't see why you're bringing in statistical mechanics here.During his productive career, Isaac Newton recognized that the level of math then was not sufficient for him to expand his work. He, therefore, went on to create and develop differential calculus (although it's argued whether he was the first to come up with it or Leibnitz, which is something I don't want to go into because it's not relevant). From what I see, based on your messages, it appears that you think the "folk" or "junk" math, as you call it, is not sufficient to tackle finance problems. If that's the case, what kind of math do you think one must use?

QuoteOriginally posted by: HensAre there any good examples where famous physical principles may be used in finance?!What about using Feynman diagrams to talk about how market transactions transfer risk and return between participants? One could think about various instruments in terms of contingent "decays" into an underlying set of cashflows to/from counterparties.

QuoteOriginally posted by: rcohenQuoteOriginally posted by: NActually Cuch, I'm quite amazed that you and cohen have no clue regarding solutions of irreducible 2nd order PDEs (eg convection-diffusion). Don't you remember Fermi, Pasta and Ulam (ULM) experiments from the early '50s where they blew apart statistical mechanics theory because the energy didn't distribute as expected into the normal modes? Applied mathematics hasn't been the same since - including major discoveries by Lax and others.Sigma algebras require the second counting axiom (aka Axioim of Choice). No credible mathematician depends on AC or uses sigma algebras."Well done"... Thanks, just doing my part to remove 'junk' math from finance.N,This needs to be straightened out - the equations (Navier-Stokes, Diffusion and Heat) are "continuous", not statistical. Navier-Stokes applies Newton's 2nd law of motion to incompressible and viscous fluids, Diffusion utilizes brownian motion as its foundation and Heat is based on the laws of conduction (Fourier) and cooling (Newton). The derivation of all of these is based on continuum assumptions. I don't see why you're bringing in statistical mechanics here.During his productive career, Isaac Newton recognized that the level of math then was not sufficient for him to expand his work. He, therefore, went on to create and develop differential calculus (although it's argued whether he was the first to come up with it or Leibnitz, which is something I don't want to go into because it's not relevant). From what I see, based on your messages, it appears that you think the "folk" or "junk" math, as you call it, is not sufficient to tackle finance problems. If that's the case, what kind of math do you think one must use?rcohenFirst, I mentioned 'statistical mechanics' since it is the math/physics of 'plain old' brownian motion. And as Fermi would have discovered (he died shortly before the results were compiled), statistical mechanics is broken - big time. I'm short, stochastic flows are inadequate to describe anything but the simplest problems (like heat flowing down a 1-D steel rod). And yeah, statistical mechanics will do to approximate simple n-body problems, but as discovered half a century ago, it's not useful for serious physics.I totally agree with you that Navier-Stokes and convection-diffusion (aka Black-Scholes) are not statistical (ie, not stochastic). In fact they are Hamiltonian flows. I'd just add that there is no relationship between these PDEs (and Hamiltionian flows in general) and normal (gaussian) distributions. So returns can't be normally distributed according to BS? Of course not... [A question for you -- is the Levy distribution really a distribution?]And as far as calculus goes, you need to understand analysis of variables before you can integrate. Real and Complex analysis address only 1/2 of the total analysis problem (all the field extensions must be handled).N

QuoteThis needs to be straightened out - the equations (Navier-Stokes, Diffusion and Heat) are "continuous", not statistical. Navier-Stokes applies Newton's 2nd law of motion to incompressible and viscous fluids, Diffusion utilizes brownian motion as its foundation and Heat is based on the laws of conduction (Fourier) and cooling (Newton). The derivation of all of these is based on continuum assumptionsRuben,I agree. And the physical motivation is well-documented as is the maths. No stochastics are needed indeed IMHO.N,QuoteA question for you -- is the Levy distribution really a distribution?What do you think? If you mean Levy processes then the DE for the security is a PIDE and this has a physical interpretation (local/non-local influence). The PDE part can be a first-order hyperbolic PDE (no volatility) and the resulting PIDE is similar to a transport equation (see the VG thread here). The physical motivation be a heat equation with memory.

QuoteOriginally posted by: NFirst, I mentioned 'statistical mechanics' since it is the math/physics of 'plain old' brownian motion. And as Fermi would have discovered (he died shortly before the results were compiled), statistical mechanics is broken - big time. I'm short, stochastic flows are inadequate to describe anything but the simplest problems (like heat flowing down a 1-D steel rod). And yeah, statistical mechanics will do to approximate simple n-body problems, but as discovered half a century ago, it's not useful for serious physics.N,Something else to clarify - I don't know what you mean by stochastic flow when you mention Navier-Stokes, although I've seen it used in the areas of turbulence and granular flows. Never the less, stochastic in the context of a stochastic differential equation has nothing to do with statistical mechanics. Statistical mechanics is a branch of thermodynamics, which led to the kinetic theory of gases and other interesting stuff. This concept comes in where the continuum assumptions break down. Basically, instead of treating a gas as continuous, statistical mechanics breaks it down into "particles" and partitions the gas into distinguishable states. It then looks for the "most probable" state. Again, this is an old area, which was originated in the late 1800s by someone called Ludwig Boltzmann. There is an interesting history behind it, which I'd strongly recommend you read about.I don't know what you're referring to when you say that Fermi et al have rubbished statistical mechanics. All I know is that you can use it to derive, in a very elegant way, all the basic energy and entropy relationships that underlie classical thermodynamics.Finally, as to your claim that the current "folk" math is not enough to tackle finance problems, I suggest that maybe you can follow up the area of statistical mechanics and see how you can find a practical use for it in finance. I have a strong feeling that there is something here that one can use constructively to study the markets.

Quotercohen:Statistical mechanics is a branch of thermodynamics, It's probably more correct to say that SM and thermodynamics are complementary: SM is the microscopic view and thermodynamics is the "external", phenomenological view. SM has been a brilliantly successful theory. As far as I'm aware there are no problems with its foundations. Mainly because it's very simple.QuoteI have a strong feeling that there is something here that one can use constructively to study the markets.I think I spotted a book on this.

QuoteOriginally posted by: INFIDELIt's probably more correct to say that SM and thermodynamics are complementary: SM is the microscopic view and thermodynamics is the "external", phenomenological view. SM has been a brilliantly successful theory. As far as I'm aware there are no problems with its foundations. Mainly because it's very simple....I think I spotted a book on this.I agree, it is probably more correct to say SM and classical thermo are complementary, since they do seem to run in parallel with each other. But the thing about it is that it's certainly brilliant!I am aware of SM being used in some areas of economics (i.e. modeling the distributions of firm sizes and earnings) but if you happen to remember the book you spotted that relates SM to finance, please let me know. Thx! RC

QuoteI think I spotted a book on thisThere's a whole slew of books on the market/stat mech interface eg., these. My impression is that the practical benefits of stat mech in finance are rather low. Mind you I've read precisely two books from the long list but stat mech seems to be a qualitative tool, I recommend instead a reading of Jan Dash's path integral book. Here at least is the very practical application of a tool from physics to finance