Agent based reasoning for the non-linear stochastic models of long-range memory

Abstract

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. Agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

Compartmental voter model

“…Some of the models were modified to account for the theories from the social sciences [12,13]. Effects of these modifications are still being actively reconsidered in context of network theory, non-linearity, complex contagion and applications towards financial markets [14][15][16][17][18][19][20][21][22][23][24][25]. Nevertheless even these modified models assume that opinion dynamics occur and are observed within single electoral unit (from here on let us also use the terms "compartment" and "spatial unit" interchangeably) over multiple time steps.…”

Output-Feedback Control for Discrete-Time Spreading Models in Complex Networks

“…Future studies will consider generalizations of this approach to higher-dimensional node dynamics, multilayer networks [42,43], complex networks of agents [44,45] and analyzing the possibility of applying these kinds of control strategies for financial market models and decision dynamics [46][47][48].…”

Interplay between Endogenous and Exogenous Fluctuations in Financial Markets

“…It was shown that such agent system is able to catch up the long range dependence of volatility [40]. The consideration of the same agent system was proposed in [49], which we adopted in a more appropriate form for our purposes and derived macroscopic (stochastic) equation for the ratio of chartists and fundamentalists x, see [50]. The main innovation was to introduce the variable trading activity of the agent system as some feedback from macroscopic state.…”

“…(9) Here α is a feedback parameter and ε 2 is idiosyncratic transition rate of chartists to fundamental behavior divided by herding parameter h, see [50] for details. As in this simplified model x has a meaning of the long-term absolute return, its power law behavior is informative about validity of such approach.…”