We show that Ito processes imply the Fokker-Planck (K2) and Kolmogorov backward time (K1) partial differential eqns. (pde) for transition densities, which in turn imply the Chapman-Kolmogorov equation without approximations. This result is not restricted to Markov processes. We define ‘finite...

There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H≠1/2 on the other. The...

Some economists (Mirowski, 2002) have asserted that the neoclassical economic model was motivated by Newtonian mechanics. This viewpoint encourages confusion. Theoretical mechanics is firmly grounded in reproducible empirical observations and experiments, and provides a very accurate description...

We provide the reader with a qualitative summary of the main ideas from econophysics and finance theory, starting with a thorough criticism of the standard ideas taught in typical economics textbooks. The emphasis is on the Galilean or physicists' approach to market synamics, as opposed to the...

This paper reports several entirely new results on financial market dynamics and option pricing We observe that empirical distributions of returns are much better approximated by an exponential distribution than by a Gaussian. This exponential distribution of asset prices can be used to develop...

Interest in thermodynamic analogies in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper we go further and use a standard strategy from trading theory...

Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are...

The discovery of the dynamics of a time series requires construction of the transition density, 1-point densities and scaling exponents provide no knowledge of the dynamics. Time series require some sort of statistical regularity, otherwise there is no basis for analysis. We state the possible...

In their path-finding 1973 paper Black and Scholes presented two separate derivations of their famous option pricing partial differential equation (pde). The second derivation was from the standpoint that was Black’s original motivation, namely, the capital asset pricing model (CAPM). We show...

General Equilibrium Theory in econometrics is based on the vague notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is sometimes treated like a potential, other times like a Lagrangian. Illegal assumptions of integrability of actions and...