Stochastic Methods from the Simplest Transaction Dynamics to the Complex Networks

In previous chapters we have seen the advent of a new society, with the growing complexity of the market and technological innovations. We demonstrated the move away from the Gaussian world towards that of heavy tail distributionHeavy tail distribution. To fully understand the latter distribution, we need to recognize a generalized central limit theoremCentral limit theorem, where the Gaussian distributionGaussian distribution is simply a special case. We are therefore able to investigate several stable distributions and expand our idea of price equilibrium as a stable distributionStable distribution. We will also discuss the central issue of how the market economy can generate complex dynamics. First, we use the simplest trader dynamicsSimplest trader dynamics system designed by Philip MayminMaymin, P.Z., and recreate his simulation dynamics for an automatonAutomaton. This explicitly takes into account traders’ decisions in combined multiple layers: actions, mind states, memories of the trader and the market. These factors are normally regarded as influential components that govern price movements. In financial transactions, we dispense with psychological effectsPsychological effects at individual and aggregate levels. These may no longer be secondary effects. We then observe the stochastic process how a complex network will be generated. Second, we then learn the multiagent trader’s dynamicsMultiagent trader’s dynamic, where the complexity of interactions between heterogeneous traders dominates the market.