engleski

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

In this paper we present the deterministic and the probabilistic model of dynamics of the price relations for a number of assets on the market. The formalism is based on the asset space introduced in the 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 the interest geometric sequence, whereas the derived probability density describes the probability of the next value of price relations in dependence on the prior value of the same. 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.

complex systems; financial markets; equilibrium dynamics; variation principle

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