Geodesic
Johansen--Sornette hierarchical model of financial crashes and its ultrametric generalization
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 162-169

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We consider the hierarchical model of financial crashes introduced by A. Johansen and D. Sornette which reproduces the log-periodic power law behavior of the price before the critical point. In order to build the generalization of this model we introduce the dependence of an influence exponent on an ultrametric distance between agents. Much attention is being paid to a problem of critical point universality which is investigated by comparison of probability density functions of the crash times corresponding to systems with various total numbers of agents.
Keywords: mathematical modeling, log-periodic power law, ultrametric distance, $p$-hierarchical structure, financial crashes. 
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     title = {Johansen--Sornette hierarchical model of financial crashes and its ultrametric generalization},
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A. S. Pivivarova; A. A. Steryakov. Johansen--Sornette hierarchical model of financial crashes and its ultrametric generalization. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 162-169. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a20/