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We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes… (More)

- V Gontis, J Ruseckas, A Kononovičius
- 2009

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the… (More)

We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some… (More)

- Aleksejus Kononovicius, Vygintas Gontis, Valentas Daniunas
- 2012

—We present examples of agent-based and stochas-tic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirman and Bass diffusion of new products… (More)

- V Gontis, B Kaulakys
- 2006

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the… (More)

- V Gontis, B Kaulakys, J Ruseckas
- 2008

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochas-tic differential equation provides the universal description of the trading activities with the same… (More)

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of… (More)

- A Kononovicius, V Gontis
- 2015

• We introduce a fixed number of controlled agents into the agent-based herding model. • The impact of the controlled agents depends only on their number. • The proposed model may be considered as an explanation of the leadership phenomenon. a b s t r a c t Collective behavior of the complex socioeconomic systems is heavily influenced by the herding, group,… (More)

- A Kononovicius, V Gontis
- 2012

We propose a Markov jump process with the three state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute… (More)

- Vygintas Gontis, Aleksejus Kononovicius, Stefan Reimann
- 2012

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multi-plicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the… (More)