Epstein Secrets

tically, however recent work by Lorenz, Paltridge, Ackland & Gallagher, and others in the field of planetary ecology and, also that of Dewar, Levy, Solomon and others in the field of theoretical physics appear to have changed things substantially. In the 1970s Garth Paltridge produced papers looking at

andom walk process has been removed from it's many body background, and individual prices are treated as moving randomly isolated by themselves. But Black-Scholes is simply the diffusion equation, and things don't diffuse with random jumps in a vacuum. The random movements of dust particles undergoing Brownia

that this chaotic motion is noticeable in objects as large as planets. This is not simply the chaos of quantum effects or the stochasticity found in Black-Scholes. This is 'deterministic chaos' or usually 'chaos theory'. The chaos is present even in problems that can be described in exact mathematics and are

despite appearing to have general applicability. The ideas of Paltridge, Lorenz, Dewar and others, along with the mathematical techniques of Levy & Solomon, may not be familiar to many physicists, and I believe may be very powerful in the analysis of complex 'out of equilibrium' systems in general. In

ists working in finance have not only accepted this, but they have built more and more baroque models on these flimsy foundations. The trouble with Black-Scholes is that it works very well, except when it doesn't. This basic flaw has been pointed out from Mandlebrot onwards, to date with no notice taken. Thi

model both the power law tails and the 'clustered volatility'. Analytic approaches have so far been less successful. However, in a series of papers, Solomon and co-workers' 8 have suggested that a very wide class of simple microscopic representation models based on generalised Lotka-Volterra (GLV) dynam

uctuations. Their continued use seems to emanate from the development of the Ito stochastic calculus that facilitated the development of the famous Black-Scholes equation used to model financial derivatives. Conversely the fitting of stock fluctuations by Levy distributions overestimates the extent of the fl