The multi-dimensional stochastic Stefan financial model for a portfolio of assets

The financial model proposed involves the liquidation process of a portfolio through sell / buy orders placed at price \begin{document}$ x\in\mathbb{R}^n $\end{document}, with volatility. Its rigorous mathematical formulation results to an id="M3">\begin{document}$ n $\end{document}-dimensional outer parabolic Stefan problem noise. The moving boundary encloses areas zero trading. We will focus on case interest when one or more markets are considered. estimate trading diameter approximating minimum id="M4">\begin{document}$ $\end{document} spreads for from limit order books. In dimensions id="M5">\begin{document}$ = 3 volatility, this stands as mean field Ostwald ripening, and has been analyzed by Niethammer in [25], rid="b7">7]. propose spherical boundaries approach where area consists union domains centered portfolios various prices radii representing half spread. apply Itô calculus provide second formal asymptotics stochastic dynamics that seem disconnect large diffusion assumption liquidity coefficient Laplacian would correspond increased density. Moreover, we solve systems numerically.