6,282 research outputs found
Pricing the implicit contracts in the Paris Club debt buybacks
In 2005, more than 20 billion dollars were bought back by Paris Club debtors: Russia USD 15 billion Poland USD 5.4 billion and Peru USD 1.5 billion. During the first half of 2006, more than USD 30 billion in buybacks was announced: Russia USD 22 billion, Algeria USD 8 billion dollars, Brazil USD 1.5 billion. The buybacks consisted of the prepayment of debts at par with no penalties. These transactions were carried out at a discount of more than 20% compared to their net present value. The total loss incurred by creditors in the three buybacks is estimated at more than USD 10 billion. This raises the question as to why the Paris Club creditors agreed to the buybacks voluntarily. It appears that these buybacks are the result of the exercise of specific contracts previously agreed with the debtors in the 1990s, without receiving any compensation for this and without assessing the consequences. These implicit contracts make it possible to formalise the respective interests for creditors and debtors. Their pricing requires the use of financial mathematics tools (derivatives) and stochastic models for interest rates (Vasicek), but applied in the Paris Club framework.buyback; Paris Club; par value; Vasicek model; creditor cartel
Statistics of non-interacting bosons and fermions in micro-canonical, canonical and grand-canonical ensembles: A survey
The statistical properties of non-interacting bosons and fermions confined in
trapping potentials are most easily obtained when the system may exchange
energy and particles with a large reservoir (grand-canonical ensemble). There
are circumstances, however, where the system under consideration may be
considered as being isolated (micro-canonical ensemble). This paper first
reviews results relating to micro-canonical ensembles. Some of them were
obtained a long time ago, particularly by Khinchin in 1950. Others were
obtained only recently, often motivated by experimental results relating to
atomic confinement. A number of formulas are reported for the first time in the
present paper. Formulas applicable to the case where the system may exchange
energy but not particles with a reservoir (canonical ensemble) are derived from
the micro-canonical ensemble expressions. The differences between the three
ensembles tend to vanish in the so-called Thermodynamics limit, that is, when
the number of particles and the volume go to infinity while the particle number
density remains constant. But we are mostly interested in systems of moderate
size, often referred to as being mesoscopic, where the grand-canonical
formalism is not applicable. The mathematical results rest primarily on the
enumeration of partitions of numbers.Comment: 18 pages, submitted to J. Phys.
Modified logarithmic Sobolev inequalities and transportation inequalities
We present a class of modified logarithmic Sobolev inequality, interpolating
between Poincar\'e and logarithmic Sobolev inequalities, suitable for measures
of the type \exp(-|x|^\al) or more complex \exp(-|x|^\al\log^\beta(2+|x|))
(\al\in]1,2[ and \be\in\dR) which lead to new concentration inequalities.
These modified inequalities share common properties with usual logarithmic
Sobolev inequalities, as tensorisation or perturbation, and imply as well
Poincar\'e inequality. We also study the link between these new modified
logarithmic Sobolev inequalities and transportation inequalities
A simple quantum heat engine
Quantum heat engines employ as working agents multi-level systems instead of
gas-filled cylinders. We consider particularly two-level agents such as
electrons immersed in a magnetic field. Work is produced in that case when the
electrons are being carried from a high-magnetic-field region into a
low-magnetic-field region. In watermills, work is produced instead when some
amount of fluid drops from a high-altitude reservoir to a low-altitude
reservoir. We show that this purely mechanical engine may in fact be considered
as a two-level quantum heat engine, provided the fluid is viewed as consisting
of n molecules of weight one and N-n molecules of weight zero. Weight-one
molecules are analogous to electrons in their higher energy state, while
weight-zero molecules are analogous to electrons in their lower energy state.
More generally, fluids consist of non-interacting molecules of various weights.
It is shown that, not only the average value of the work produced per cycle,
but also its fluctuations, are the same for mechanical engines and quantum
(Otto) heat engines. The reversible Carnot cycles are approached through the
consideration of multiple sub-reservoirs.Comment: RevTeX 9 pages, 4 figures, paper shortened, improved presentatio
Comment on: "Sadi Carnot on Carnot's theorem"
Carnot established in 1824 that the efficiency of reversible
engines operating between a hot bath at absolute temperature and a
cold bath at temperature is equal to . Carnot
particularly considered air as a working fluid and small bath-temperature
differences. Plugging into Carnot's expression modern experimental values,
exact agreement with modern Thermodynamics is found. However, in a recently
published paper ["Sadi Carnot on Carnot's theorem", \textit{Am. J. Phys.}
\textbf{70}(1), 42-47, 2002], Guemez and others consider a "modified cycle"
involving two isobars that they mistakenly attribute to Carnot. They calculate
an efficiency considerably lower than and suggest that Carnot made
compensating errors. Our contention is that the Carnot theory is, to the
contrary, perfectly accurate.Comment: Submitted to American Journal of Physic
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