Assessing black swan events with the stochastic least action principle, Tsallis entropy and heavy-tailed distribution

Abstract

We present a formulation of the Stochastic Least Action Principle which encompasses random movements describing black swan events of non-dissipative systems in terms of heavy-tailed distributions. Black swan events are rare and drastic episodes such as earthquakes and financial crisis. We showed that black swan events of physical systems are proportional to nonlocal correlations, thus making the Tsallis entropy more appropriate for its description rather than the conventional Shannon-Boltzman-Gibbs entropy. As a consequence, we assessed the validity of the path probability distribution obtained using the non-additive Tsallis entropy.