Modelling stock markets by probabilistic 1-D cellular automata

Abstract

The concept of probabilistic cellular automata is introduced in this paper. The automata are used to model a simple stock market in which the buying and selling of a stock is governed by a probabilistic transition function which is also a function of time. It is possible to apply theories of Markov chain, e.g. absorption time, to this situation. Some popular strategies of investing in a stock market can also be simulated by the cellular automaton models with appropriate transition functions.

Keywords:

• Cellular automata
• transition function
• Markov chain
• Correlation dimension