841 research outputs found
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio
We use a continuous version of the standard deviation premium principle for
pricing in incomplete equity markets by assuming that the investor issuing an
unhedgeable derivative security requires compensation for this risk in the form
of a pre-specified instantaneous Sharpe ratio. First, we apply our method to
price options on non-traded assets for which there is a traded asset that is
correlated to the non-traded asset. Our main contribution to this particular
problem is to show that our seller/buyer prices are the upper/lower good deal
bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko
(2006) and to determine the analytical properties of these prices. Second, we
apply our method to price options in the presence of stochastic volatility. Our
main contribution to this problem is to show that the instantaneous Sharpe
ratio, an integral ingredient in our methodology, is the negative of the market
price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar
(2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe
ratio, correlated assets, stochastic volatility, non-linear partial
differential equations, good deal bound
Some extremal functions in Fourier analysis, III
We obtain the best approximation in , by entire functions of
exponential type, for a class of even functions that includes
, where , and , where . We also give periodic versions of these results where the
approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte
Deterministic delivery of externally cold and precisely positioned single molecular ions
We present the preparation and deterministic delivery of a selectable number
of externally cold molecular ions. A laser cooled ensemble of Mg^+ ions
subsequently confined in several linear Paul traps inter-connected via a
quadrupole guide serves as a cold bath for a single or up to a few hundred
molecular ions. Sympathetic cooling embeds the molecular ions in the
crystalline structure. MgH^+ ions, that serve as a model system for a large
variety of other possible molecular ions, are cooled down close to the Doppler
limit and are positioned with an accuracy of one micrometer. After the
production process, severely compromising the vacuum conditions, the molecular
ion is efficiently transfered into nearly background-free environment. The
transfer of a molecular ion between different traps as well as the control of
the molecular ions in the traps is demonstrated. Schemes, optimized for the
transfer of a specific number of ions, are realized and their efficiencies are
evaluated. This versatile source applicable for broad charge-to-mass ratios of
externally cold and precisely positioned molecular ions can serve as a
container-free target preparation device well suited for diffraction or
spectroscopic measurements on individual molecular ions at high repetition
rates (kHz).Comment: 11 pages, 8 figure
Operator renewal theory and mixing rates for dynamical systems with infinite measure
We develop a theory of operator renewal sequences in the context of infinite
ergodic theory. For large classes of dynamical systems preserving an infinite
measure, we determine the asymptotic behaviour of iterates of the
transfer operator. This was previously an intractable problem.
Examples of systems covered by our results include (i) parabolic rational
maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly
expanding interval maps with indifferent fixed points.
In addition, we give a particularly simple proof of pointwise dual ergodicity
(asymptotic behaviour of ) for the class of systems under
consideration.
In certain situations, including Pomeau-Manneville intermittency maps, we
obtain higher order expansions for and rates of mixing. Also, we obtain
error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a
minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated
version includes minor corrections in Sections 10 and 11, and corresponding
modifications of certain statements in Section 1. All main results are
unaffected. In particular, Sections 2-9 are unchanged from the published
versio
Solidification of Al-Sn-Cu based immiscible alloys under intense shearing
The official published version of the Article can be accessed from the link below - Copyright @ 2009 The Minerals, Metals & Materials Society and ASM InternationalThe growing importance of Al-Sn based alloys as materials for engineering applications
necessitates the development of uniform microstructures with improved performance. Guided by the recently thermodynamically assessed Al-Sn-Cu system, two model immiscible alloys, Al-45Sn-10Cu and Al-20Sn-10Cu, were selected to investigate the effects of intensive melt shearing provided by the novel melt conditioning by advanced shear technology (MCAST) unit on the uniform dispersion of the soft Sn phase in a hard Al matrix. Our experimental results have confirmed that intensive melt shearing is an effective way to achieve fine and uniform
dispersion of the soft phase without macro-demixing, and that such dispersed microstructure can be further refined in alloys with precipitation of the primary Al phase prior to the demixing reaction. In addition, it was found that melt shearing at 200 rpm and 60 seconds will be adequate to produce fine and uniform dispersion of the Sn phase, and that higher shearing speed and prolonged shearing time can only achieve minor further refinement.This work is funded by the EPSRC and
DT
Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux
in various dimensions. We realize the backgrounds as supercosets and analyze
explicitly two classes of models: non-critical superstrings on AdS_{2d} and
critical superstrings on AdS_p\times S^p\times CY. We work both in the
Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter
family of flat currents (a Lax connection) leading to an infinite number of
conserved non-local charges, which imply the classical integrability of both
sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove
the quantum integrability of the sigma-model. We discuss how classical
\kappa-symmetry implies one-loop conformal invariance. We consider the addition
of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos
fixed in some equations; v3: typos fixed to match the published versio
High-precision determination of transition amplitudes of principal transitions in Cs from van der Waals coefficient C_6
A method for determination of atomic dipole matrix elements of principal
transitions from the value of dispersion coefficient C_6 of molecular
potentials correlating to two ground-state atoms is proposed. The method is
illustrated on atomic Cs using C_6 deduced from high-resolution Feshbach
spectroscopy. The following reduced matrix elements are determined < 6S_{1/2}
|| D || 6P_{1/2} > =4.5028(60) |e| a0 and
=6.3373(84) |e| a0 (a0= 0.529177 \times 10^{-8} cm.) These matrix elements are
consistent with the results of the most accurate direct lifetime measurements
and have a similar uncertainty. It is argued that the uncertainty can be
considerably reduced as the coefficient C_6 is constrained further.Comment: 4 pages; 3 fig
Generic properties of a quasi-one dimensional classical Wigner crystal
We studied the structural, dynamical properties and melting of a
quasi-one-dimensional system of charged particles, interacting through a
screened Coulomb potential. The ground state energy was calculated and,
depending on the density and the screening length, the system crystallizes in a
number of chains. As a function of the density (or the confining potential),
the ground state configurations and the structural transitions between them
were analyzed both by analytical and Monte Carlo calculations. The system
exhibits a rich phase diagram at zero temperature with continuous and
discontinuous structural transitions. We calculated the normal modes of the
Wigner crystal and the magneto-phonons when an external constant magnetic field
is applied. At finite temperature the melting of the system was studied via
Monte Carlo simulations using the (MLC). The
melting temperature as a function of the density was obtained for different
screening parameters. Reentrant melting as a function of the density was found
as well as evidence of directional dependent melting. The single chain regime
exhibits anomalous melting temperatures according to the MLC and as a check we
study the pair correlation function at different densities and different
temperatures, formulating a different criterion. Possible connection with
recent theoretical and experimental results are discussed and experiments are
proposed.Comment: 13 pages text, 21 picture
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