2,102 research outputs found
Volatility and dividend risk in perpetual American options
American options are financial instruments that can be exercised at any time
before expiration. In this paper we study the problem of pricing this kind of
derivatives within a framework in which some of the properties --volatility and
dividend policy-- of the underlaying stock can change at a random instant of
time, but in such a way that we can forecast their final values. Under this
assumption we can model actual market conditions because some of the most
relevant facts that may potentially affect a firm will entail sharp predictable
effects. We will analyse the consequences of this potential risk on perpetual
American derivatives, a topic connected with a wide class of recurrent problems
in physics: holders of American options must look for the fair price and the
optimal exercise strategy at once, a typical question of free absorbing
boundaries. We present explicit solutions to the most common contract
specifications and derive analytical expressions concerning the mean and higher
moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep
revision, two new appendice
The fundamental plane of evolving red nuggets
We present an exploration of the mass structure of a sample of 12 strongly
lensed massive, compact early-type galaxies at redshifts to provide
further possible evidence for their inside-out growth. We obtain new ESI/Keck
spectroscopy and infer the kinematics of both lens and source galaxies, and
combine these with existing photometry to construct (a) the fundamental plane
(FP) of the source galaxies and (b) physical models for their dark and luminous
mass structure. We find their FP to be tilted towards the virial plane relative
to the local FP, and attribute this to their unusual compactness, which causes
their kinematics to be totally dominated by the stellar mass as opposed to
their dark matter; that their FP is nevertheless still inconsistent with the
virial plane implies that both the stellar and dark structure of early-type
galaxies is non-homologous. We also find the intrinsic scatter of their FP to
be comparable to the local value, indicating that variations in the stellar
mass structure outweight variations in the dark halo in the central regions of
early-type galaxies. Finally, we show that inference on the dark halo structure
-- and, in turn, the underlying physics -- is sensitive to assumptions about
the stellar initial mass function (IMF), but that physically-motivated
assumptions about the IMF imply haloes with sub-NFW inner density slopes, and
may present further evidence for the inside-out growth of compact early-type
galaxies via minor mergers and accretion.Comment: 10 pages, 3 figures, 3 tables; submitted to MNRA
Mass along the Line of Sight to the Gravitational Lens B1608+656: Galaxy Groups and Implications for H_0
We report the discovery of four groups of galaxies along the line of sight to the B1608+656 gravitational lens system. One group is at the redshift of the primary lensing galaxy (z = 0.631) and appears to have a low mass, with eight spectroscopically confirmed members and an estimated velocity dispersion of 150 ± 60 km s^(-1). The three other groups are in the foreground of the lens. These groups contain ~10 confirmed members each and are located at redshifts of 0.265, 0.426, and 0.52. Two of the three additional groups are centered roughly on the lens system, while the third is centered ~1' south of the lens. We investigate the effect of each of the four groups on the gravitational lensing potential of the B1608+656 system, with a particular focus on the implications for the value of H_0 derived from this system. We find that each group provides an external convergence of ~0.005-0.060, depending on the assumptions made in the calculation. For the B1608+656 system, the stellar velocity dispersion of the lensing galaxy has been measured, thus breaking the mass sheet degeneracy due to the group that is physically associated with the lens. The effect of the other groups along the line of sight can be folded into the overall uncertainties due to large-scale structure (LSS) along the line of sight. Because B1608+656 appears to lie along an overdense line of sight, the LSS will cause the measurement of H_0 to be biased high for this system. This effect could be 5% or greater
Long term Arecibo monitoring of the water megamaser in MG J0414+0534
We monitored the 22 GHz maser line in the lensed quasar MG J0414+0534 at
z=2.64 with the 300-m Arecibo telescope for almost two years to detect possible
additional maser components and to measure a potential velocity drift of the
lines. The main maser line profile is complex and can be resolved into a number
of broad features with line widths of 30-160 km/s. A new maser component was
tentatively detected in October 2008 at a velocity of +470 km/s. After
correcting for the estimated lens magnification, we find that the H2O isotropic
luminosity of the maser in MG J0414+0534 is about 26,000 solar luminosities,
making this source the most luminous ever discovered. Both the main line peak
and continuum flux densities are surprisingly stable throughout the period of
the observations. An upper limit on the velocity drift of the main peak of the
line has been estimated from our observations and is of the order of 2 km/s per
year. We discuss the results of the monitoring in terms of the possible nature
of the maser emission, associated with an accretion disk or a radio jet. This
is the first time that such a study is performed in a water maser source at
high redshift, potentially allowing us to study the parsec-scale environment
around a powerful radio source at cosmological distances.Comment: 5 pages, 2 figures, to appear in the Proceedings of the IAU Symposium
287, 2012, "Cosmic masers: from OH to H0
Keck spectroscopy of CLASS gravitational lenses
We present the optical spectra of four newly discovered gravitational lenses
from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried
out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope
as part of a program to study galaxy-scale gravitational lenses. From our
spectra we found the redshift of the background source in CLASS B0128+437
(z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123
(z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we
also discovered that CLASS B0631+519 may have two lensing galaxies
(z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single
unidentified emission line from the lensing galaxy in CLASS B0128+437 and the
lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS
B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein
Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type
galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA
2-D constrained Navier-Stokes equation and intermediate asymptotics
We introduce a modified version of the two-dimensional Navier-Stokes
equation, preserving energy and momentum of inertia, which is motivated by the
occurrence of different dissipation time scales and related to the gradient
flow structure of the 2-D Navier-Stokes equation. The hope is to understand
intermediate asymptotics. The analysis we present here is purely formal. A
rigorous study of this equation will be done in a forthcoming paper
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