DVA for Assets

The effect of self-default on the valuation of liabilities and derivatives (DVA) has been widely discussed but the effect on assets has not received similar attention. Any asset whose value depends on the status, or existence, of the firm will have a DVA. We extend (Burgard and Kjaer 2011) to provide a hedging strategy for such assets and provide an in-depth example from the balance sheet (Goodwill). We calibrate our model to seven US banks over the crisis period of mid-2007 to 2011. This suggests that their reported profits would have changed significantly if DVA on assets, as well as liabilities, was included - unless the DVA was hedged.Comment: 16 pages, 4 figure

Coagulation Calculations of Icy Planet Formation at 15--150 AU: A Correlation Between the Maximum Radius and the Slope of the Size Distribution for Transneptunian Objects

We investigate whether coagulation models of planet formation can explain the observed size distributions of transneptunian objects (TNOs). Analyzing published and new calculations, we demonstrate robust relations between the size of the largest object and the slope of the size distribution for sizes 0.1 km and larger. These relations yield clear, testable predictions for TNOs and other icy objects throughout the solar system. Applying our results to existing observations, we show that a broad range of initial disk masses, planetesimal sizes, and fragmentation parameters can explain the data. Adding dynamical constraints on the initial semimajor axis of `hot' KBOs along with probable TNO formation times of 10-700 Myr restricts the viable models to those with a massive disk composed of relatively small (1-10 km) planetesimals.Comment: Text: 44 pages, Tables: 5, Figures: 17; Accepted for publication in the Astronomical Journa

The asymptotic determinant of the discrete Laplacian

We compute the asymptotic determinant of the discrete Laplacian on a simply-connected rectilinear region in R^2. As an application of this result, we prove that the growth exponent of the loop-erased random walk in Z^2 is 5/4.Comment: 36 pages, 4 figures, to appear in Acta Mathematic