214 research outputs found
Dam Rain and Cumulative Gain
We consider a financial contract that delivers a single cash flow given by
the terminal value of a cumulative gains process. The problem of modelling and
pricing such an asset and associated derivatives is important, for example, in
the determination of optimal insurance claims reserve policies, and in the
pricing of reinsurance contracts. In the insurance setting, the aggregate
claims play the role of the cumulative gains, and the terminal cash flow
represents the totality of the claims payable for the given accounting period.
A similar example arises when we consider the accumulation of losses in a
credit portfolio, and value a contract that pays an amount equal to the
totality of the losses over a given time interval. An explicit expression for
the value process is obtained. The price of an Arrow-Debreu security on the
cumulative gains process is determined, and is used to obtain a closed-form
expression for the price of a European-style option on the value of the asset.
The results obtained make use of various remarkable properties of the gamma
bridge process, and are applicable to a wide variety of financial products
based on cumulative gains processes such as aggregate claims, credit portfolio
losses, defined-benefit pension schemes, emissions, and rainfall.Comment: 25 Pages, 1 Figur
Exclusive Queueing Process with Discrete Time
In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of
the M/M/1 queueing process with the excluded-volume effect as in the totally
asymmetric simple exclusion process (TASEP) was introduced. In this paper, we
consider its discrete-time version. The update scheme we take is the parallel
one. A stationary-state solution is obtained in a slightly arranged matrix
product form of the discrete-time open TASEP with the parallel update. We find
the phase diagram for the existence of the stationary state. The critical line
which separates the parameter space into the regions with and without the
stationary state can be written in terms of the stationary current of the open
TASEP. We calculate the average length of the system and the average number of
particles
Branching processes, the max-plus algebra and network calculus
Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
International audienceThis chapter proposes a framework for dealing with two problems related to the analysis of shapes: the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and ZolĂ©sio [8], we consider the characteristic functions of the subsets of â2 and their distance functions. The L 2 norm of the difference of characteristic functions and the Lâ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular that induced by the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of â2 of positive reach in the sense of Federer [12], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding GĂąteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem. We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational de.nitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples
Shape Space Methods for Quantum Cosmological Triangleland
With toy modelling of conceptual aspects of quantum cosmology and the problem
of time in quantum gravity in mind, I study the classical and quantum dynamics
of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do
so by importing techniques to the triangle model from the corresponding 4
particles in 1-d model, using the fact that both have 2-spheres for shape
spaces, though the latter has a trivial realization whilst the former has a
more involved Hopf (or Dragt) type realization. I furthermore interpret the
ensuing Dragt-type coordinates as shape quantities: a measure of
anisoscelesness, the ellipticity of the base and apex's moments of inertia, and
a quantity proportional to the area of the triangle. I promote these quantities
at the quantum level to operators whose expectation and spread are then useful
in understanding the quantum states of the system. Additionally, I tessellate
the 2-sphere by its physical interpretation as the shape space of triangles,
and then use this as a back-cloth from which to read off the interpretation of
dynamical trajectories, potentials and wavefunctions. I include applications to
timeless approaches to the problem of time and to the role of uniform states in
quantum cosmological modelling.Comment: A shorter version, as per the first stage in the refereeing process,
and containing some new reference
Some functional equations related to the characterizations of information measures and their stability
The main purpose of this paper is to investigate the stability problem of
some functional equations that appear in the characterization problem of
information measures.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1307.0657,
arXiv:1307.0631, arXiv:1307.0664, arXiv:1307.065
Experimental support of the scaling rule for demographic stochasticity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73613/1/j.1461-0248.2006.00903.x.pd
Electromagnetic Polarization Effects due to Axion Photon Mixing
We investigate the effect of axions on the polarization of electromagnetic
waves as they propagate through astronomical distances. We analyze the change
in the dispersion of the electromagnetic wave due to its mixing with axions. We
find that this leads to a shift in polarization and turns out to be the
dominant effect for a wide range of frequencies. We analyze whether this effect
or the decay of photons into axions can explain the large scale anisotropies
which have been observed in the polarizations of quasars and radio galaxies. We
also comment on the possibility that the axion-photon mixing can explain the
dimming of distant supernovae.Comment: 18 pages, 1 figur
Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping
The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided
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