Model of discrete dynamics of asset price relations based on the minimal arbitrage principle

• Authors: Zvonko Kostanjčar , Kristian Hengster-Movrić , Branko Jeren
• Languages of publication: EN

Abstracts

EN

In this paper we present a deterministic and a probabilistic model of the dynamics of the price relations for a number of assets on the market. The formalism is based on the asset space introduced in a theory by Illinski. We derive, from an action functional for the system of price relations in that space, the corresponding difference equations, which constitute the deterministic description. Furthermore, we obtain the probability density function of the probabilistic model of market dynamics from the same action functional. The deterministic solution corresponds to a geometric sequence for the interest, whereas the derived probability density describes the probability of the next value of the price relations in dependence on their prior value. The formalism is completely developed for systems (markets) with two and three assets, but exactly the same approach is applicable to the systems consisting of an arbitrary number of assets.

Keywords

EN

complex systems; financial markets; equilibrium dynamics; variation principle

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 3
• Pages: 865-873

Dates

published

1 - 6 - 2011

online

26 - 2 - 2011

Contributors

author

Zvonko Kostanjčar

• Department of Electronic Systems and Information Processing, University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, HR-10000, Zagreb, Croatia

author

Kristian Hengster-Movrić

• Advanced Controls and Sensors Group, University of Texas at Arlington, 701 S. Nedderman Drive, Arlington, TX, 76019, USA

author

Branko Jeren

• Department of Electronic Systems and Information Processing, University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, HR-10000, Zagreb, Croatia

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Identifiers

DOI

10.2478/s11534-010-0093-x