32,189 research outputs found
The SuperB factory: Physics Prospects and Project Status
I will briefly review of some highlights of the SuperB physics programme, the
status of the accelerator and detector studies, and the future plans.Comment: 6 pages, 0 figures, contribution to the Physics in Collision 2012
(PIC2012) conference. arXiv admin note: substantial text overlap with
arXiv:1112.1394, arXiv:1012.244
On the optimality of Periodic barrier strategies for a spectrally positive L\'evy process
We study the optimal dividend problem in the dual model where dividend
payments can only be made at the jump times of an independent Poisson process.
In this context, Avanzi et al. [5] solved the case with i.i.d. hyperexponential
jumps; they showed the optimality of a (periodic) barrier strategy where
dividends are paid at dividend-decision times if and only if the surplus is
above some level. In this paper, we generalize the results for a general
spectrally positive Levy process with additional terminal payoff/penalty at
ruin, and also solve the case with classical bail-outs so that the surplus is
restricted to be nonnegative. The optimal strategies as well as the value
functions are concisely written in terms of the scale function. Numerical
results are also given.Comment: To appear on Insurance: Mathematics and Economic
-jumping and -Jacobian ideals for hypersurfaces
We introduce two families of ideals, -jumping ideals and -Jacobian
ideals, in order to study the singularities of hypersurfaces in positive
characteristic. Both families are defined using the -modules
that were introduced by Blickle, Musta\c{t}\u{a} and Smith. Using strong
connections between -jumping ideals and generalized test ideals, we give a
characterization of -jumping numbers for hypersurfaces. Furthermore, we give
an algorithm that determines whether certain numbers are -jumping numbers.
In addition, we use -Jacobian ideals to study intrinsic properties of the
singularities of hypersurfaces. In particular, we give conditions for
-regularity. Moreover, -Jacobian ideals behave similarly to Jacobian
ideals of polynomials. Using techniques developed to study these two new
families of ideals, we provide relations among test ideals, generalized test
ideals, and generalized Lyubeznik numbers for hypersurfaces.Comment: References updated, 32 page
Refraction-reflection strategies in the dual model
We study the dual model with capital injection under the additional condition
that the dividend strategy is absolutely continuous. We consider a
refraction-reflection strategy that pays dividends at the maximal rate whenever
the surplus is above a certain threshold, while capital is injected so that it
stays positive. The resulting controlled surplus process becomes the spectrally
positive version of the refracted-reflected process recently studied by P\'erez
and Yamazaki (2015). We study various fluctuation identities of this process
and prove the optimality of the refraction-reflection strategy. Numerical
results on the optimal dividend problem are also given.Comment: 33 page
On the Refracted-Reflected Spectrally Negative L\'evy Processes
We study a combination of the refracted and reflected L\'evy processes. Given
a spectrally negative L\'evy process and two boundaries, it is reflected at the
lower boundary while, whenever it is above the upper boundary, a linear drift
at a constant rate is subtracted from the increments of the process. Using the
scale functions, we compute the resolvent measure, the Laplace transform of the
occupation times as well as other fluctuation identities that will be useful in
applied probability including insurance, queues, and inventory management.Comment: 28 pages, forthcoming in Stochastic Processes and their Application
Universality classes for general random matrix flows
We consider matrix-valued processes described as solutions to stochastic
differential equations of very general form. We study the family of the
empirical measure-valued processes constructed from the corresponding
eigenvalues. We show that the family indexed by the size of the matrix is tight
under very mild assumptions on the coefficients of the initial SDE. We
characterize the limiting distributions of its subsequences as solutions to an
integral equation. We use this result to study some universality classes of
random matrix flows. These generalize the classical results related to Dyson
Brownian motion and squared Bessel particle systems. We study some new
phenomenons as the existence of the generalized Marchenko-Pastur distributions
supported on the real line. We also introduce universality classes related to
generalized geometric matrix Brownian motions and Jacobi processes. Finally we
study, under some conditions, the convergence of the empirical measure-valued
process of eigenvalues associated to matrix flows to the law of a free
diffusion.Comment: 27 page
On the Free Fractional Wishart Process
We investigate the process of eigenvalues of a fractional Wishart process
defined as N=B*B, where B is a matrix fractional Brownian motion recently
studied by Nualart and P\'erez-Abreu. Using stochastic calculus with respect to
the Young integral we show that the eigenvalues do not collide at any time with
probability one. When the matrix process B has entries given by independent
fractional Brownian motions with Hurst parameter we derive a
stochastic differential equation in a Malliavin calculus sense for the
eigenvalues of the corresponding fractional Wishart process. Finally a
functional limit theorem for the empirical measure-valued process of
eigenvalues of a fractional Wishart process is obtained. The limit is
characterized and referred to as the free fractional Wishart process which
constitutes the family of fractional dilations of the free Poisson
distribution
American options under periodic exercise opportunities
In this paper, we study a version of the perpetual American call/put option
where exercise opportunities arrive only periodically. Focusing on the
exponential L\'evy models with i.i.d. exponentially-distributed exercise
intervals, we show the optimality of a barrier strategy that exercises at the
first exercise opportunity at which the asset price is above/below a given
barrier. Explicit solutions are obtained for the cases the underlying L\'evy
process has only one-sided jumps
A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion
A functional limit theorem for the empirical measure-valued process of
eigenvalues of a matrix fractional Brownian motion is obtained. It is shown
that the limiting measure-valued process is the non-commutative fractional
Brownian motion recently introduced by Nourdin and Taqqu. Young and Skorohod
stochastic integral techniques and fractional calculus are the main tools used
On the intersection graph of the disks with diameters the sides of a convex -gon
Given a convex -gon, we can draw disks (called side disks) where each
disk has a different side of the polygon as diameter and the midpoint of the
side as its center. The intersection graph of such disks is the undirected
graph with vertices the disks and two disks are adjacent if and only if
they have a point in common. Such a graph was introduced by Huemer and
P\'erez-Lantero in 2016, proved to be planar and Hamiltonian. In this paper we
study further combinatorial properties of this graph. We prove that the
treewidth is at most 3, by showing an -time algorithm that builds a tree
decomposition of width at most 3, given the polygon as input. This implies that
we can construct the intersection graph of the side disks in time. We
further study the independence number of this graph, which is the maximum
number of pairwise disjoint disks. The planarity condition implies that for
every convex -gon we can select at least pairwise
disjoint disks, and we prove that for every there exist convex
-gons in which we cannot select more than this number. Finally, we show that
our class of graphs includes all outerplanar Hamiltonian graphs except the
cycle of length four, and that it is a proper subclass of the planar
Hamiltonian graphs
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