Crashes : symptoms, diagnoses and remedies

Abstract

A brief historical perspective is first given concerning financial crashes, -from the 17th till the 20th century. In modern times, it seems that log periodic oscillations are found before crashes in several financial indices. The same is found in sand pile avalanches on Sierpinski gaskets. A discussion pertains to the after shock period with illustrations from the DAX index. The factual financial observations and the laboratory ones allow us some conjecture on symptoms and remedies for discussing financial crashes along econophysics lines.

Can we predict crashes? The case of the Brazilian stock market

“…Johansen et al [3] analyzed eight unrelated crashes from 1929 to 1998 and concluded that no major financial crash preceded by an extended bubble has occurred in the past two decades without exhibiting a log-periodic signature. Ausloos et al [14] admitted that signals of crashes can be found in terms of power laws and oscillations to suggest remedies to control or avoid crashes. Suggestions are: reduce the number of orders, impose some delay in the orders, increase the number of actors on the market together with a decrease in exchanged volume.…”

“…Ausloos and Ivanova [14,4] demonstrated, using the envelope of the Deutsche Aktien IndeX (DAX), that a log-periodic pattern exists before a crash. Their model considers huge fluctuations grouped around the crash date (increased volatility), collective effects leading to a bear market and a strong correlation found in fluctuations of different market indices before crashes.…”

A Stochastic Pontryagin Maximum Principle on the Sierpinski Gasket

“…Several interesting mathematical finance problems are formulated as stochastic control problems on Euclidean spaces, which are based upon the assumption that uncertainties in financial models are sourced from Brownian filtration on Euclidean spaces. However, it had been widely observed from the real data that many financial time series exhibit fractal behaviours (see, for example, [1,8,2] and etc. ), which suggests the possibility that uncertainties in the markets might come from filtrations exhibiting fractal structures.…”

World Financial 2014-2016 Market Bubbles: Oil Negative - US Dollar Positive

“…In spite of rising some controversies [7][8][9], many successful attempts to describe [10][11][12][13][14][15][16][17][18][19][20][21][22] and even to detect bubbles and their subsequent bursts by using this technique [23][24][25][26] have been reported. One of the most spectacular such examples is ex ante exceptionally precise prediction of Brent Crude Oil bubble bursting time in early July 2008, delivered three months ahead as described in Ref.…”