Government intervention modeling in microeconomic company market evolution

Modern technology and innovations are becoming more crucial than ever for the survival of companies in the market. Therefore, it is significant both from theoretical and practical points of view to understand how governments can influence technology growth and innovation diffusion (TGID) processes. We propose a simple but essential extension of Ausloos-Clippe-Pc{e}kalski and related Cichy numerical models of the TGID in the market. Both models are inspired by the nonlinear non-equilibrium statistical physics. Our extension involves a parameter describing the probability of government intervention in the TGID process in the company market. We show, using Monte Carlo simulations, the effects interventionism can have on the companies market, depending on the segment of firms that are supported. The high intervention probability can result, paradoxically, in the destabilization of the market development. It lowers the markets technology level in the long-time limit compared to markets with a lower intervention parameter. We found that the intervention in the technologically weak and strong segments of the company market does not substantially influence the market dynamics, compared to the intervention helping the middle-level companies. However, this is still a simple model which can be extended further and made more realistic by including other factors. Namely, the cost and risk of innovation or limited government resources and capabilities to support companies.

Agent-Based Stock Market Model with Endogenous Agents Impact

The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three fundamental stylised facts: fat-tail log returns, power-law volatility autocorrelation decay in time and volatility clustering.

Continuous-Time Random Walk with multi-step memory: An application to market dynamics

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.

Reinterpretation of Sieczka-Ho{l}yst financial market model

In this work we essentially reinterpreted the Sieczka-Ho{l}yst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the SH model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.

Trust in foreseeing neighbours - a novel threshold model of financial market

The three-state agent-based 2D model of financial markets in the version proposed by Giulia Iori in 2002 has been herein extended. We have introduced the increase of herding behaviour by modelling the altering trust of an agent in his nearest neighbours. The trust increases if the neighbour has foreseen the price change correctly and the trust decreases in the opposite case. Our version only slightly increases the number of parameters present in the Iori model. This version well reproduces the main stylized facts observed on financial markets. That is, it reproduces log-returns clustering, fat-tail log-returns distribution and power-law decay in time of the volatility autocorrelation function.

Super-extreme events influence on a Weierstrass-Mandelbrot Continuous-Time Random Walk

Two utmost cases of super-extreme events influence on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism, which is able to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of a sustained drift, whose duration time is much longer than that of any other event. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of these super-extreme events substantially changes the results determined by extreme events (the so called black swans) that are endogenous to the WM-CTRW process. For example, changes of the VAF in the latter case are in the form of some instability and distinctly differ from those caused in the former case. In each case these changes are quite different compared to the situation without super-extreme events suggesting the possibility to detect them in natural system if they occur.