Macrodynamics

Field characteristic

Economic dynamics and macroeconomic modelling

Nonlinear model of closed economy is formulated on an extended and modified Kaldor's model of small closed economy with a simple structure and several nonlinearities. Nonlinear pattern of dependencies in this model is created by a logistic function. The model is realized by four differential equations. The first equation and second equation describe output and capital dynamics. A core of the output dynamics is formulated by investment and savings disequilibrium. Capital dynamics is formed by a net investment. The third equation describes price dynamics through disequilibrium powers on monetary markets. And the fourth equation describes expected inflation formulated as an adaptive expectation. Behavior analysis of this model is realized on numerical calibrated model. The considered model demonstrates chaotic solution of attractors by positive Lyapunov exponent. Kaldor's model is described in some classical macroeconomics.

A simple dynamic continuous nonlinear model for the description and investigate the possibility of more complex behaviour of such systems was chosen. The stability such systems was tested and Lyapunov exponents were computed using appropriate numerical methods.

Heterogeneous Agents Models

Previous model with Worst Out Algorithm (WOA) in heterogeneous agents model on financial markets was modified. The important outcome of the simulations was a possibility of a prediction in the case with the normally distributed memory length of agents presented on the financial market (normal case). An interesting result concerning risk behavior was the fact that the WOA plays a stabilizing role in the normal case in a sense of decreasing variance in time. Conversely, the uniform case (uniformly distributed memory length of agents presented on the financial market) affects the financial market risk level negatively, i.e., rising variance in time.

Capital Market Theory

Main attention was paid to the order driven markets with asynchronous trading. As a first step of his long term research, the markets with completely random behavior of the agents and with the unit order sizes were studied. Even if the order driven markets are regarded as analytically intractable, two closed form results were achieved in this area: the first one being the analytical formula for the conditional distribution of the limit order book given the history of the best quote process. The second one being an arbitrarily exact approximation of the joint distribution of the market price and the traded volume.

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Selected publications

Grants and projects