Free boundary on a cone

We study two phase problems posed over a two dimensional cone generated by a smooth curve $\gamma$ on the unit sphere. We show that when $length(\gamma)<2\pi$ the free boundary avoids the vertex of the cone. When $length(\gamma) \geq 2\pi$ we provide examples of minimizers such that the vertex belongs to the free boundary

Information acquisition and financial contagion.

This paper incorporates costly voluntary acquisition of information à la Nikitin and Smith (2007) [Nikitin, M., Smith, R.T., 2007. Information acquisition, coordination, and fundamentals in a financial crisis. Journal of Banking and Finance, in press, doi:10.1016/j.jbankfin.2007.04.031], in a framework similar to Allen and Gale (2000) [Allen, F., Gale, D., 2000. Financial contagion. Journal of Political Economy 108, 1–33], without relying on any unexpected shock to model contagion. In this framework, contagion and financial crises are the result of information gathering by depositors, weak fundamentals and an incomplete market structure of banks. It also shows how financial systems entering a recession can affect others with apparently stronger economic conditions (contagion). Finally, this is the first paper to investigate the effectiveness of the Contingent Credit Line procedures, introduced by the IMF at the end of the nineties, as a mechanism to prevent the propagation of crises.Central Bank; Contingent credit line; Financial contagion; Fundamentals; Verification equilibrium;

Extreme Graphical Models with Applications to Functional Neuronal Connectivity

With modern calcium imaging technology, the activities of thousands of neurons can be recorded simultaneously in vivo. These experiments can potentially provide new insights into functional connectivity, defined as the statistical relationships between the spiking activity of neurons in the brain. As a commonly used tool for estimating conditional dependencies in high-dimensional settings, graphical models are a natural choice for analyzing calcium imaging data. However, raw neuronal activity recording data presents a unique challenge: the important information lies in the rare extreme value observations that indicate neuronal firing, as opposed to the non-extreme observations associated with inactivity. To address this issue, we develop a novel class of graphical models, called the extreme graphical model, which focuses on finding relationships between features with respect to the extreme values. Our model assumes the conditional distributions a subclass of the generalized normal or Subbotin distribution, and yields a form of a curved exponential family graphical model. We first derive the form of the joint multivariate distribution of the extreme graphical model and show the conditions under which it is normalizable. We then demonstrate the model selection consistency of our estimation method. Lastly, we study the empirical performance of the extreme graphical model through several simulation studies as well as through a real data example, in which we apply our method to a real-world calcium imaging data set