Abstract:
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.
Citation:
A. S. Pivivarova, A. A. Steryakov, “Johansen–Sornette hierarchical model of financial crashes and its ultrametric generalization”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 162–169
\Bibitem{PivSte11}
\by A.~S.~Pivivarova, A.~A.~Steryakov
\paper Johansen--Sornette hierarchical model of financial crashes and its ultrametric generalization
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 2(23)
\pages 162--169
\mathnet{http://mi.mathnet.ru/vsgtu885}
\crossref{https://doi.org/10.14498/vsgtu885}
Linking options:
https://www.mathnet.ru/eng/vsgtu885
https://www.mathnet.ru/eng/vsgtu/v123/p162
This publication is cited in the following 1 articles:
A. A. Maiorov, A. R. Safin, “The possibility of using permanent magnets without rare earth elements in electric motors”, «Izvestiya vysshikh uchebnykh zavedenii. PROBLEMY ENERGETIKI», 24:4 (2022), 116