Towards breaking the Omega-bias degeneracy in density--velocity comparisons

I derive a second-order local relation between the REDSHIFT-space mass density field and the REAL-space velocity field. This relation can be useful for comparisons between the cosmic density and peculiar velocity fields, for a number of reasons. First, relating the real-space velocity directly to the redshift-space density enables one to avoid the Omega-dependent reconstruction of the density field in real space. Secondly, the reconstruction of the three-dimensional velocity field in redshift space, questionable because of its vorticity, is also unnecessary. Finally, a similar relation between the GALAXY density field and the velocity field offers a way to break the Omega-bias degeneracy in density--velocity comparisons, when combined with an additional measurement of the redshift-space galaxy skewness. I derive the latter relation under the assumption of nonlinear but local bias; accounting for stochasticity of bias is left for further study.Comment: 13 pages, no figures, uses mn.sty. The calculation properly redone for bias in real space, added references. Accepted by MNRA

Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion

We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. The basic model is then extended to incorporate multivariate bubbles and contagion, non-Gaussian models and models based on stochastic volatility. Only in a stochastic volatility model where the mean of the log-returns is considered fixed does volatility increase prior to a crash.Financial crashes, super-exponential growth, illusion of certainty, contagion, housing-bubble.

Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion

We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. The basic model is then extended to incorporate multivariate bubbles and contagion, non-Gaussian models and models based on stochastic volatility. Only in a stochastic volatility model where the mean of the log-returns is fixed does volatility increase prior to a crash.financial crashes; super-exponential growth; illusion of certainty; contagion

Bubbles and contagion in English house prices

Using methods originating from statistical physics we model bubbles in English house prices. It is found that there was a nationwide housing bubble 2002-2007. Typically prices were 30-40% over-valued and fell around 20%. London is atypical in that the level of over-pricing was lower, only around 20%, and experienced a drop in prices of only around 15%. There is some suggestion of contagious effects, with the bubble in London affecting prices in Yorkshire and the North.financial crashes; super-exponential growth; illusion of certainty; contagion; housing-bubble; Enlish house prices