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Keyword: Ising

Bornholdt’s heterogeneous agent based spin model for financial markets

bornholdt-fin

Previously we have discussed ant colony model 1, 2 (see Kirman’s agent based and stochastic model of ant colony), which is an interesting example of applying knowledge obtained from one field to another. Human (ex. trader in the financial markets) crowd behavior is ideologically quite similar to the behavior in ant colonies, thus the success and relevancy of the aforementioned model were to be expected. Though the key to success lies in the description of large number of entities.

Interestingly enough one can also create, and thus provide additional backing for the argument above, a successful model for human crowd behavior using classical models of statistical physics as an inspiration. In this text we will discuss agent based spin model of the financial markets proposed by Bornholdt 3, 4, which is based on widely known Ising model. Continue reading “Bornholdt’s heterogeneous agent based spin model for financial markets” »

Ising model

ising thumb

Ising model is a generalized mathematical model of feromagnetism in statistical physics. In this model particles having magnetic spin are put inside vertices of graph. In general case structure of graph can vary alot, but in the ussuall case selection is limited to the lattices of different dimensions. Behavior of such system is observed at different temperature in the quest to find critical temperature at which phase shift occurs. If you want to familarize yourself more with Ising model and it’s various interpretations, you should read 1, 2 works, because in this text we will only consider one possible, numerical, algorithm – heat bath algorithm.
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