  The financial model proposed involves the liquidation process of a portfolio
of $n$ assets through sell or (and) buy orders with volatility. We present the
rigorous mathematical formulation of this model in a financial setting
resulting to an $n$-dimensional outer parabolic Stefan problem with noise. In
particular, our aim is to estimate for a short time period the areas of zero
trading, and their diameter which approximates the minimum of the $n$ spreads
of the portfolio assets for orders from the $n$ limit order books of each asset
respectively. In dimensions $n=3$, and for zero volatility, this problem stands
as a mean field model for Ostwald ripening, and has been proposed and analyzed
by Niethammer. Therein, when the initial moving boundary consists of well
separated spheres, a first order approximation system of odes had been
rigorously derived for the dynamics of the interfaces and the asymptotic
profile of the solution. In our financial case, we propose a spherical moving
boundaries approach where the zero trading area consists of a union of
spherical domains centered at portfolios various prices, while each sphere may
correspond to a different market; the relevant radii represent the half of the
minimum spread. We apply It\^o calculus and provide second order formal
asymptotics for the stochastic version dynamics, written as a system of
stochastic differential equations for the radii evolution in time. A second
order approximation seems to disconnect the financial model from the large
diffusion assumption for the trading density. Moreover, we solve the
approximating systems numerically.
