82,556 research outputs found
Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk
For a given Markov process and survival function on
, the inverse first-passage time problem (IFPT) is to find a
barrier function such that the survival
function of the first-passage time is given
by . In this paper, we consider a version of the IFPT problem
where the barrier is fixed at zero and the problem is to find an initial
distribution and a time-change such that for the time-changed process
the IFPT problem is solved by a constant barrier at the level zero.
For any L\'{e}vy process satisfying an exponential moment condition, we
derive the solution of this problem in terms of -invariant
distributions of the process killed at the epoch of first entrance into the
negative half-axis. We provide an explicit characterization of such
distributions, which is a result of independent interest. For a given
multi-variate survival function of generalized frailty type, we
construct subsequently an explicit solution to the corresponding IFPT with the
barrier level fixed at zero. We apply these results to the valuation of
financial contracts that are subject to counterparty credit risk.Comment: Published at http://dx.doi.org/10.1214/14-AAP1051 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Utility based pricing and hedging of jump diffusion processes with a view to applications
We discuss utility based pricing and hedging of jump diffusion processes with
emphasis on the practical applicability of the framework. We point out two
difficulties that seem to limit this applicability, namely drift dependence and
essential risk aversion independence. We suggest to solve these by a
re-interpretation of the framework. This leads to the notion of an implied
drift. We also present a heuristic derivation of the marginal indifference
price and the marginal optimal hedge that might be useful in numerical
computations.Comment: 23 pages, v2: publishe
Streaming velocities as a dynamical estimator of Omega
It is well known that estimating the pairwise velocity of galaxies, v_{12},
from the redshift space galaxy correlation function is difficult because this
method is highly sensitive to the assumed model of the pairwise velocity
dispersion. Here we propose an alternative method to estimate v_{12} directly
from peculiar velocity samples, which contain redshift-independent distances as
well as galaxy redshifts. In contrast to other dynamical measures which
determine beta = sigma_8 x Omega^{0.6}, our method can provide an estimate of
(sigma_8)^2 x Omega^{0.6} for a range of sigma_8 (here Omega is the
cosmological mass density parameter while sigma_8 is the standard normalization
parameter for the spectrum of matter density fluctuations). We demonstrate how
to measure this quantity from realistic catalogues.Comment: 8 pages of text, 4 figures Subject headings: Cosmology: theory -
observation - peculiar velocities: large scale flows Last name of one of the
authors was misspelled. It is now corrected. Otherwise the manuscript is
identical to its original versio
Measuring Omega with Galaxy Streaming Velocities
The mean pairwise velocity of galaxies has traditionally been estimated from
the redshift space galaxy correlation function. This method is notorious for
being highly sensitive to the assumed model of the pairwise velocity
dispersion. Here we propose an alternative method to estimate the streaming
velocity directly from peculiar velocity samples, which contain
redshift-independent distances as well as galaxy redshifts. This method can
provide an estimate of for a range of where
is the cosmological density parameter, while is the
standard normalization for the power spectrum of density fluctuations. We
demonstrate how to measure this quantity from realistic catalogues and identify
the main sources of bias and errorsComment: Proceedings of New Worlds in Astroparticle Physics, 6 pages, 2
figure
Evidence for a low-density Universe from the relative velocities of galaxies
The motions of galaxies can be used to constrain the cosmological density
parameter Omega and the clustering amplitude of matter on large scales. The
mean relative velocity of galaxy pairs, estimated from the Mark III survey,
indicates that Omega = 0.35 +0.35/-0.25. If the clustering of galaxies is
unbiased on large scales, Omega = 0.35 +/- 0.15, so that an unbiased
Einstein-de Sitter model (Omega = 1) is inconsistent with the data.Comment: 12 pages, 2 figures, to appear in the Jan.7 issue of ``Science''; In
the original version, the title appeared twice. This problem has now been
corrected. No other changes were mad
Inference on the tail process with application to financial time series modelling
To draw inference on serial extremal dependence within heavy-tailed Markov
chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed
nonparametric estimators of the spectral tail process. The methodology can be
extended to the more general setting of a stationary, regularly varying time
series. The large-sample distribution of the estimators is derived via
empirical process theory for cluster functionals. The finite-sample performance
of these estimators is evaluated via Monte Carlo simulations. Moreover, two
different bootstrap schemes are employed which yield confidence intervals for
the pre-asymptotic spectral tail process: the stationary bootstrap and the
multiplier block bootstrap. The estimators are applied to stock price data to
study the persistence of positive and negative shocks.Comment: 22 page
Determination of the gaseous hydrogen ductile-brittle transition in copper-nickel alloys
A series of copper-nickel alloys were fabricated, notched tensile specimens machined for each alloy, and the specimens tested in 34.5 MPa hydrogen and in air. A notched tensile ratio was determined for each alloy and the hydrogen environment embrittlement (HEE) determined for the alloys of 47.7 weight percent nickel to 73.5 weight percent nickel. Stacking fault probability and stacking fault energies were determined for each alloy using the x ray diffraction line shift and line profiles technique. Hydrogen environment embrittlement was determined to be influenced by stacking fault energies; however, the correlation is believed to be indirect and only partially responsible for the HEE behavior of these alloys
Fermion zero modes in N=2 supervortices
We study the fermionic zero modes of BPS semilocal magnetic vortices in N=2
supersymmetric QED with a Fayet-Iliopoulos term and two matter hypermultiplets
of opposite charge. There is a one-parameter family of vortices with
arbitrarily wide magnetic cores. Contrary to the situation in pure
Nielsen-Olesen vortices, new zero modes are found which get their masses from
Yukawa couplings to scalar fields that do not wind and are non-zero at the
core. We clarify the relation between fermion mass and zero modes. The new zero
modes have opposite chiralities and therefore do not affect the net counting
(left minus right) of zero modes coming from index theorems but manage to evade
other index theorems in the literature that count the total number (left plus
right) of zero modes in simpler systems.Comment: 9 pages, 1 figure. Uses Revtex4. Revised version includes discussion
about the back-reaction of the fermions on the background vortex. Version to
be published in Phys. Rev.
Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects
We use the dynamics of a galaxy, set up initially at a constant proper
distance from an observer, to derive and illustrate two counter-intuitive
general relativistic results. Although the galaxy does gradually join the
expansion of the universe (Hubble flow), it does not necessarily recede from
us. In particular, in the currently favored cosmological model, which includes
a cosmological constant, the galaxy recedes from the observer as it joins the
Hubble flow, but in the previously favored cold dark matter model, the galaxy
approaches, passes through the observer, and joins the Hubble flow on the
opposite side of the sky. We show that this behavior is consistent with the
general relativistic idea that space is expanding and is determined by the
acceleration of the expansion of the universe -- not a force or drag associated
with the expansion itself. We also show that objects at a constant proper
distance will have a nonzero redshift; receding galaxies can be blueshifted and
approaching galaxies can be redshifted.Comment: 8 pages including 6 figures, to appear in Am. J. Phys., 2003.
Reference added in postscrip
Computable functions, quantum measurements, and quantum dynamics
We construct quantum mechanical observables and unitary operators which, if
implemented in physical systems as measurements and dynamical evolutions, would
contradict the Church-Turing thesis which lies at the foundation of computer
science. We conclude that either the Church-Turing thesis needs revision, or
that only restricted classes of observables may be realized, in principle, as
measurements, and that only restricted classes of unitary operators may be
realized, in principle, as dynamics.Comment: 4 pages, REVTE
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