In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

In a recent article [1], the authors report evidence for an intriguing two-phase behavior of financial markets when studying the distribution of volume imbalance (Ω) conditional to the local intensity of its fluctuations (Σ). We show here that this apparent phase transition is a generic consequence of the conditioning and exists even in the absence of any non trivial collective phenomenon. More...