1,757 research outputs found
E-finance-lab at the House of Finance : about us
The financial services industry is believed to be on the verge of a dramatic [r]evolution. A substantial redesign of its value chains aimed at reducing costs, providing more efficient and flexible services and enabling new products and revenue streams is imminent. But there seems to be no clear migration path nor goal which can cast light on the question where the finance industry and its various players will be and should be in a decade from now. The mission of the E-Finance Lab is the development and application of research methodologies in the financial industry that promote and assess how business strategies and structures are shared and supported by strategies and structures of information systems. Important challenges include the design of smart production infrastructures, the development and evaluation of advantageous sourcing strategies and smart selling concepts to enable new revenue streams for financial service providers in the future. Overall, our goal is to contribute methods and views to the realignment of the E-Finance value chain. ..
Brownian motion in a truncated Weyl chamber
We examine the non-exit probability of a multidimensional Brownian motion
from a growing truncated Weyl chamber. Different regimes are identified
according to the growth speed, ranging from polynomial decay over
stretched-exponential to exponential decay. Furthermore we derive associated
large deviation principles for the empirical measure of the properly rescaled
and transformed Brownian motion as the dimension grows to infinity. Our main
tool is an explicit eigenvalue expansion for the transition probabilities
before exiting the truncated Weyl chamber
Large deviations for the local times of a random walk among random conductances in a growing box
We derive an annealed large deviation principle (LDP) for the normalised and
rescaled local times of a continuous-time random walk among random conductances
(RWRC) in a time-dependent, growing box in . We work in the interesting
case that the conductances are positive, but may assume arbitrarily small
values. Thus, the underlying picture of the principle is a joint strategy of
small conductance values and large holding times of the walk. The speed and the
rate function of our principle are explicit in terms of the lower tails of the
conductance distribution as well as the time-dependent size of the box.
An interesting phase transition occurs if the thickness parameter of the
conductance tails exceeds a certain threshold: for thicker tails, the random
walk spreads out over the entire growing box, for thinner tails it stays
confined to some bounded region. In fact, in the first case, the rate function
turns out to be equal to the -th power of the -norm of the gradient of
the square root for some . This extends the
Donsker-Varadhan-G\"artner rate function for the local times of Brownian motion
(with deterministic environment) from to these values.
As corollaries of our LDP, we derive the logarithmic asymptotics of the
non-exit probability of the RWRC from the growing box, and the Lifshitz tails
of the generator of the RWRC, the randomised Laplace operator.
To contrast with the annealed, not uniformly elliptic case, we also provide
an LDP in the quenched setting for conductances that are bounded and bounded
away from zero. The main tool here is a spectral homogenisation result, based
on a quenched invariance principle for the RWRC.Comment: 32 page
A Gibbsian model for message routeing in highly dense multihop networks
We investigate a probabilistic model for routeing of messages in
relay-augmented multihop ad-hoc networks, where each transmitter sends one
message to the origin. Given the (random) transmitter locations, we weight the
family of random, uniformly distributed message trajectories by an exponential
probability weight, favouring trajectories with low interference (measured in
terms of signal-to-interference ratio) and trajectory families with little
congestion (measured in terms of the number of pairs of hops using the same
relay). Under the resulting Gibbs measure, the system targets the best
compromise between entropy, interference and congestion for a common welfare,
instead of an optimization of the individual trajectories.
In the limit of high spatial density of users, we describe the totality of
all the message trajectories in terms of empirical measures. Employing large
deviations arguments, we derive a characteristic variational formula for the
limiting free energy and analyse the minimizer(s) of the formula, which
describe the most likely shapes of the trajectory flow. The empirical measures
of the message trajectories well describe the interference, but not the
congestion; the latter requires introducing an additional empirical measure.
Our results remain valid under replacing the two penalization terms by more
general functionals of these two empirical measures.Comment: 40 page
The longest excursion of a random interacting polymer
We consider a random -step polymer under the influence of an attractive
interaction with the origin and derive a limit law -- after suitable shifting
and norming -- for the length of the longest excursion towards the Gumbel
distribution. The embodied law of large numbers in particular implies that the
longest excursion is of order long. The main tools are taken from
extreme value theory and renewal theory.Comment: 5 page
Geometric characterization of intermittency in the parabolic Anderson model
We consider the parabolic Anderson problem on
with localized initial condition
and random i.i.d. potential . Under the assumption
that the distribution of has a double-exponential, or slightly
heavier, tail, we prove the following geometric characterization of
intermittency: with probability one, as , the overwhelming
contribution to the total mass comes from a slowly increasing
number of ``islands'' which are located far from each other. These ``islands''
are local regions of those high exceedances of the field in a box of side
length for which the (local) principal Dirichlet eigenvalue of the
random operator is close to the top of the spectrum in the box. We
also prove that the shape of in these regions is nonrandom and that
is close to the corresponding positive eigenfunction. This is the
geometric picture suggested by localization theory for the Anderson
Hamiltonian.Comment: Published at http://dx.doi.org/10.1214/009117906000000764 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Moment asymptotics for multitype branching random walks in random environment
We study a discrete time multitype branching random walk on a finite space
with finite set of types. Particles follow a Markov chain on the spatial space
whereas offspring distributions are given by a random field that is fixed
throughout the evolution of the particles. Our main interest lies in the
averaged (annealed) expectation of the population size, and its long-time
asymptotics. We first derive, for fixed time, a formula for the expected
population size with fixed offspring distributions, which is reminiscent of a
Feynman-Kac formula. We choose Weibull-type distributions with parameter
for the upper tail of the mean number of type particles
produced by an type particle. We derive the first two terms of the
long-time asymptotics, which are written as two coupled variational formulas,
and interpret them in terms of the typical behavior of the system
Annealed deviations of random walk in random scenery
Let be a -dimensional {\it random walk in random
scenery}, i.e.,
with a random walk in
and an i.i.d. scenery, independent of the walk. The
walker's steps have mean zero and finite variance. We identify the speed and
the rate of the logarithmic decay of for various choices
of sequences in . Depending on and the upper
tails of the scenery, we identify different regimes for the speed of decay and
different variational formulas for the rate functions. In contrast to recent
work \cite{AC02} by A. Asselah and F. Castell, we consider sceneries {\it
unbounded} to infinity. It turns out that there are interesting connections to
large deviation properties of self-intersections of the walk, which have been
studied recently by X. Chen \cite{C03}.Comment: 32 pages, revise
Large deviations for cluster size distributions in a continuous classical many-body system
An interesting problem in statistical physics is the condensation of
classical particles in droplets or clusters when the pair-interaction is given
by a stable Lennard-Jones-type potential. We study two aspects of this problem.
We start by deriving a large deviations principle for the cluster size
distribution for any inverse temperature and particle
density in the thermodynamic limit. Here
is the close packing density. While in general the rate
function is an abstract object, our second main result is the
-convergence of the rate function toward an explicit limiting rate
function in the low-temperature dilute limit ,
such that for some
. The limiting rate function and its minimisers appeared in
recent work, where the temperature and the particle density were coupled with
the particle number. In the decoupled limit considered here, we prove that just
one cluster size is dominant, depending on the parameter . Under
additional assumptions on the potential, the -convergence along curves
can be strengthened to uniform bounds, valid in a low-temperature, low-density
rectangle.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1014 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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