Stochastic Control 2010
DOI: 10.5772/9748
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A Non-Linear Double Stochastic Model of Return in Financial Markets

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Cited by 11 publications
(35 citation statements)
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References 27 publications
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“…The proposed consentaneous agent-based and stochastic model of the financial markets is a result of our previous research in stochastic modeling, see references in [25,41], and agent-based modeling of herding interaction [33,34].…”
Section: Discussionmentioning
confidence: 99%
“…The proposed consentaneous agent-based and stochastic model of the financial markets is a result of our previous research in stochastic modeling, see references in [25,41], and agent-based modeling of herding interaction [33,34].…”
Section: Discussionmentioning
confidence: 99%
“…This provides an evidence that proposed noisy three state herding model can reproduce empirical statistics of return in financial market in very details. From our point of view this result is considerable step in stochastic modeling of financial markets in comparison with previous modeling [8,9], as incorporates microscopic model of agents and exogenous noise of information flow.…”
Section: Exogenous Information Flow Noisementioning
confidence: 87%
“…In [8,9], while relying on the empirical analysis, we have assumed that the return, r t (T ), fluctuates as instantaneous q-Gaussian noise ξ[r 0 (x), λ] with λ = 5 and driven by some stochastic process x(t). The function r 0 (x) has a linear form…”
Section: Exogenous Information Flow Noisementioning
confidence: 99%
“…(5) suggests that it is possible to obtain other values of the power law exponent β as long as η ̸ = 1. In our previous work we have shown that η > 1 cases work very well for the modeling of high-frequency trading activity as well as high-frequency absolute returns of the financial markets [35,53,54], although theoretically η < 1 is also possible [34]. One can obtain the η > 1 case by considering the following modifications of GARCH(1,1) process:…”
Section: Nonlinear Garch(11) Process Generating Signals With 1/f Noisementioning
confidence: 96%