16,413 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
General scalar products in the arbitrary six-vertex model
In this work we use the algebraic Bethe ansatz to derive the general scalar
product in the six-vertex model for generic Boltzmann weights. We performed
this calculation using only the unitarity property, the Yang-Baxter algebra and
the Yang-Baxter equation. We have derived a recurrence relation for the scalar
product. The solution of this relation was written in terms of the domain wall
partition functions. By its turn, these partition functions were also obtained
for generic Boltzmann weights, which provided us with an explicit expression
for the general scalar product.Comment: 24 page
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory
In this article we obtain a fundamental measure functional for the model of
aligned hard hexagons in the plane. Our aim is not just to provide a functional
for a new, admittedly academic, model, but to investigate the structure of
fundamental measure theory. A model of aligned hard hexagons has similarities
with the hard disk model. Both share "lost cases", i.e. admit configurations of
three particles in which there is pairwise overlap but not triple overlap.
These configurations are known to be problematic for fundamental measure
functionals, which are not able to capture their contribution correctly. This
failure lies in the inability of these functionals to yield a correct low
density limit of the third order direct correlation function. Here we derive
the functional by projecting aligned hard cubes on the plane x+y+z=0. The
correct dimensional crossover behavior of these functionals permits us to
follow this strategy. The functional of aligned hard cubes, however, does not
have lost cases, so neither had the resulting functional for aligned hard
hexagons. The latter exhibits, in fact, a peculiar structure as compared to the
one for hard disks. It depends on a uniparametric family of weighted densities
through a new term not appearing in the functional for hard disks. Apart from
studying the freezing of this system, we discuss the implications of the
functional structure for new developments of fundamental measure theory.Comment: 10 pages, 9 figures, uses RevTeX
Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
We discuss an algebraic method for constructing eigenvectors of the transfer
matrix of the eight vertex model at the discrete coupling parameters. We
consider the algebraic Bethe ansatz of the elliptic quantum group for the case where the parameter satisfies for arbitrary integers , and . When or
is odd, the eigenvectors thus obtained have not been discussed previously.
Furthermore, we construct a family of degenerate eigenvectors of the XYZ spin
chain, some of which are shown to be related to the loop algebra
symmetry of the XXZ spin chain. We show that the dimension of some degenerate
eigenspace of the XYZ spin chain on sites is given by , if
is an even integer. The construction of eigenvectors of the transfer matrices
of some related IRF models is also discussed.Comment: 19 pages, no figure (revisd version with three appendices
Quantum channels in random spin chains
We study the entanglement between pairs of qubits in a random
antiferromagnetic spin-1/2 chain at zero temperature. We show that some very
distant pairs of qubits are highly entangled, being almost pure Bell states.
Furthermore, the probability to obtain such spin pairs is proportional to the
chain disorder strenght and inversely proportional to the square of their
separation.Comment: v1: 4 pages, 2 eps figures; v2: discussion about the effect of
temperature added, v3: 1 eps figure added, enlarged discussions, 6 pages,
published versio
Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
An integrable self-adjoint 7-point scheme on the triangular lattice and an
integrable self-adjoint scheme on the honeycomb lattice are studied using the
sublattice approach. The star-triangle relation between these systems is
introduced, and the Darboux transformations for both linear problems from the
Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A
geometric interpretation of the Laplace transformations of the self-adjoint
7-point scheme is given and the corresponding novel integrable discrete 3D
system is constructed.Comment: 15 pages, 6 figures; references added, some typos correcte
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
Double Potts chain and exact results for some two-dimensional models
A closed-form exact analytical solution for the q-state Potts model on a
ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit
cell is presented. Using the obtained solution it is shown that the finite-size
internal energy equation yields an accurate value of the critical temperature
for the triangular Potts lattice with three-site interactions in alternate
triangular faces. It is argued that the above equation is exact at least for
self-dual models on isotropic lattices.Comment: 13 pages in latex and 2 ps figures. preprint ICTP IC/2000/176; ZhETF
120 (2001) (in press
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