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Table 1 Model terms

From: Analysing the behavioural finance impact of 'fake news' phenomena on financial markets: a representative agent model and empirical validation

\(P\) Security valuation for the representative agent
\(t\) Time period
\(I_{n}\) News shock conveying an unambiguous security value at time \(n\)
\(n \in \left\{ {0, \ldots ,M} \right\}\) Period, \(t = n\), when news shock \(I_{n}\) occurred
\(j \in \left\{ {0, \ldots ,M\left| j \right\rangle n} \right\}\) Period, \(t = j\), when news shock \(I_{{j > n}}\) occurred
\(\theta _{n} \in \left[ {0,1} \right]\) Weighted share of news shock \(I_{n}\);\(~\mathop \sum \limits_{{n = 0}}^{M} \theta _{n} = 1\)
\(S_{n} \ge 0\) Information weight of news shock \(I_{n}\)
\(\omega _{n} \in \left\{ {0,1} \right\}\) Real or fake news indicator for \(I_{n}\); information credibility
\(\rho \in \left[ {0.5,1} \right]\) Ability to distinguish between real and fake news
\(\rho _{0} \in \left[ {0.5,1} \right]\) Initial ability to distinguish between real and fake news
\(\delta \in \left[ {0,1} \right]\) Irrelevance multiplier of old news shocks
\(\varphi \in \left[ {0,1} \right]\) Time decay factor of spurious information
\(\alpha \ge 1\) Virality factor of fake news
\(\gamma \in \left\{ {0,1} \right\}\) Signalled presence of fake news indicator
\(\mu \in \left[ {0,1} \right]\) Fake news uncertainty factor