Kirman’s ant colony model, previously presented on our website as agent based (based on 1) and stochastic (based on 2, 3) model, has become classical example of herding modeling. Application of this model towards economic, financial or other social scenarios might seem doubtful as human society is far more complex than ant colony, but methodologically it is more useful to start from very simple and stylized model and later add complexity on top of it. Furthermore we have already shown that Kirman’s herding dynamics could be applicable in agent based marketing (see comparison of Kirman’s and Bass diffusion model). In this text we will consider financial market scenario and obtain stochastic differential equations similar to the existing stochastic models considered in 4, 5. Continue reading “Agent based herding model of financial markets” »
Previously on Physics of Risk website we have presented Kirman’s ant colony agent based model 1, where each ant was represented as an agent. In this article we will move from the agent based model framework to the stochastic differential equation framework. Thus showing that in case of simple agent based models full transition to stochastic framework is possible. This transition is very important as stochastic framework is very popular and well developed in quantitative finance. The problem is that stochastic framework mainly gives only a macroscopic insight into the modeled system, while microscopic behavior currently is also of big interest.
Continue reading “Stochastic ant colony model” »
There is an interesting phenomenon concerning behavior of ant colony. It appears that if there are two identical food sources nearby, ants exploit only one of them at a given time. The interesting thing is that used food source is not certain at any point of time. At some times switch between food sources occur though the quality of food sources remains the same. In 1993 Alan Kirman proposed that this could happen due to importance of herding behavior in ant colonies 1. Continue reading “Kirman’s ant colony model” »