Abstract
In this paper, we introduce a simple interactive agent mechanism, where the distribution of returns generated from the mechanism match stylized facts in financial markets. We introduce one more key factor, the length of time horizon on performance evaluations between strategies, which also has a significant influence on price fluctuations. To investigate the transitions among states, we introduce a Markov transition matrix, Perron‐Frobenius transition matrix, and Inertia. Our simulation results show the stickiness of states switching from one to another, and the longer length of time horizon on performance evaluations would generate more complex dynamic price fluctuations. We link our simple heterogeneous agent mechanism with Markov trajectory entropy and provide a total score and probability density functions of representations under two states as applications for the mechanism.
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Notes
Here we set \(\varepsilon _{{1,t}} \sim N\left( {0,1} \right)\) and \(\varepsilon _{{2,t}}\) varies with different distributions: \(N\left( {0,1} \right)\), \(t\left( {\upsilon = 5} \right)\),
\({\text{stable}}\left( {\alpha = 1.5,\beta = 0,\sigma = 1,\mu = 0} \right)\), GARCH normal with \(\alpha _{0} = 0,\alpha _{1} = 0.9,\beta _{1} = 0.05\), GARCH t.
with \(\upsilon = 5,\alpha _{0} = 0,\alpha _{1} = 0.9,\beta _{1} = 0.05\), GJR t with \(\upsilon = 5,\alpha _{0} = 0,\alpha _{1} = 0.9,\beta _{1} = 0.05,\gamma = 0.1\),
FIGARCH (1,d,1) normal with \(\omega = 0.05,\alpha = 0.05,d = 0.4,\beta = 0.45\) and FIGARCH (1,d,1) t.
with \(\upsilon = 5,\omega = 0.05,\alpha = 0.05,d = 0.4,\beta = 0.45\).
Here 0.1 is the threshold \(\vartheta\) to induce fundamentalists having reaction responding to the popularity of their strategy.
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Cheng, PK. Transitions among states behind interactive agent model. Comput Math Organ Theory 28, 27–51 (2022). https://doi.org/10.1007/s10588-021-09337-w
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DOI: https://doi.org/10.1007/s10588-021-09337-w