Complexity research draws on complexity in various disciplines. This Handbook provides a comprehensive and current overview of applications of complexity theory in economics. The 15 chapters, written by leading figures in the field, cover such broad topic areas as conceptual issues,...

We show by explicit closed form calculations that a Hurst exponent H≠12 does not necessarily imply long time correlations like those found in fractional Brownian motion (fBm). We construct a large set of scaling solutions of Fokker–Planck partial differential equations (pdes) where H≠12....

The distribution of price returns is studied for a class of market models with Markovian dynamics. The models have a non-constant diffusion coefficient that depends on the value of the return. An analytical expression for the distribution of returns is obtained, and shown to match the results of...

This reply addresses the assertion in the comment of T.D. Frank [T.D. Frank, Physica A 387 (2008) 773] on our paper [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343] that the approach to modeling financial markets that we propose is unrealistic. In our paper, we considered...

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 fractional Brownian motion (fBm) on the one hand and Gaussian Markov processes where...

The discovery of the dynamics of a time series requires construction of the transition density. We explain why 1-point densities and scaling exponents cannot determine the class of stochastic dynamics. Time series require some sort of underlying statistical regularity to provide a basis for...

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...

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...