Macro-prudential regulation of credit booms and busts -- the case of Poland

The last several years before the global downturn of 2008-2009 saw rapid credit growth in Poland. The credit-to-gross domestic product ratio rose from about 25 percent in 2004 to close to 50 percent in 2009. Such an expansionitself might potentially be a source of risks to financial stability, but it was also coupled with relatively new phenomena, such as massive foreign currency lending. Thanks to the pro-active attitude of the Polish authorities and sound economic fundamentals, the risks largely have not materialized. Since 2006 the financial supervisor has addressed in its recommendations for banks the problem of foreign exchange lending, which contributed to the high quality of the portfolio. Before the economy slowed down, the Polish Financial Supervisory Authority persuaded banks to accumulate an additional capital buffer that helped protect them from the negative consequences of the downturn. Some regulatory concepts that had been put into place in Poland in the previous years, including quantitative liquidity requirements, are now being implemented globally. The Polish Financial Supervisory Authority participates in international debates on a new regulatory regime for the financial system. The major message the authority intends to convey is that all new regulations must be tailored carefully. Regulators should make an effort to ensure that the benefits of enhanced quality of the capital base or the countercyclical buffer are not compromised by international overregulation that could undermine national authorities'ability to pursue effective country-specific policies.Banks&Banking Reform,Debt Markets,Access to Finance,Bankruptcy and Resolution of Financial Distress,Emerging Markets

Study of the Equilibria of Parabolic Differential Equations with Interfaces Intersecting the Boundary

Existence of steady state solutions for the Allen-Cahn and Cahn-Hilliard equations in two dimensional domains is discussed. We are in particular interested in establishing existence of single layered equilibria with the property that their transition layer intersects the boundary. In the case of the Allen-Cahn equation we consider bone-like domains and seek solutions intersecting the flat part of the boundary. We establish conditions for the domain which ensure existence of such equilibria. Their stability is also analyzed. For the Cahn-Hilliard equations we show that there exist equilibria near every point of a local maximum of the curvature of the boundary

Interface Foliation Near Minimal Submanifolds in Riemannian Manifolds with Positive Ricci Curvature

Let (\MM ,{\tilde g}) be an $N$-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation \epsilon^2\Delta_{ {\tilde g}} {u}\,+\, (1 - {u}^2)u \,=\,0\quad \mbox{in } \MM, where $\epsilon$ is a small parameter. Let \KK\subset \MM be an $(N-1)$-dimensional smooth minimal submanifold that separates \MM into two disjoint components. Assume that \KK is non-degenerate in the sense that it does not support non-trivial Jacobi fields, and that |A_{\KK}|^2+\mbox{Ric}_{\tilde g}(\nu_{\KK}, \nu_{\KK}) is positive along \KK. Then for each integer $m\geq 2$, we establish the existence of a sequence $\epsilon = \epsilon_j\to 0$, and solutions $u_{\epsilon}$ with $m$-transition layers near \KK, with mutual distance $O(\epsilon |\ln \epsilon|)$.Comment: accepted in GAF

Maximal solution of the Liouville equation in doubly connected domains

In this paper we consider the Liouville equation $\Delta u +\lambda^2 e^{\,u}=0$ with Dirichlet boundary conditions in a two dimensional, doubly connected domain $\Omega$. We show that there exists a simple, closed curve $\gamma\subset \Omega$ such that for a sequence $\lambda_n\to 0$ and a sequence of solutions $u_{n}$ it holds $\frac{u_{n}}{\log\frac{1}{\lambda_n}}\to H$, where $H$ is a harmonic function in $\Omega\setminus\gamma$ and $\frac{\lambda_n^2}{\log\frac{1}{\lambda_n}}\int_\Omega e^{\,u_n}\,dx\to 8\pi c_\Omega$, where $c_\Omega$ is a constant depending on the conformal class of $\Omega$ only