21,604 research outputs found
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
The Collisional Divot in the Kuiper belt Size Distribution
This paper presents the results of collisional evolution calculations for the
Kuiper belt starting from an initial size distribution similar to that produced
by accretion simulations of that region - a steep power-law large object size
distribution that breaks to a shallower slope at r ~1-2 km, with collisional
equilibrium achieved for objects r ~0.5 km. We find that the break from the
steep large object power-law causes a divot, or depletion of objects at r
~10-20 km, which in-turn greatly reduces the disruption rate of objects with r>
25-50 km, preserving the steep power-law behavior for objects at this size. Our
calculations demonstrate that the roll-over observed in the Kuiper belt size
distribution is naturally explained as an edge of a divot in the size
distribution; the radius at which the size distribution transitions away from
the power-law, and the shape of the divot from our simulations are consistent
with the size of the observed roll-over, and size distribution for smaller
bodies. Both the kink radius and the radius of the divot center depend on the
strength scaling law in the gravity regime for Kuiper belt objects. These
simulations suggest that the sky density of r ~1 km objects is ~10^6-10^7
objects per square degree. A detection of the divot in the size distribution
would provide a measure of the strength of large Kuiper belt objects, and
constrain the shape of the size distribution at the end of accretion in the
Kuiper belt.Comment: 32 pages, 10 figures, accepted to the Astrophysical Journa
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