Forward-Invariance and Wong-Zakai Approximation for Stochastic Moving Boundary Problems

We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution remains negative on one side and positive on the other side of the moving interface, when started with the appropriate initial conditions. To extend results from deterministic settings to the stochastic case, we establish a Wong-Zakai type approximation. After a coordinate transformation the problems are reformulated and analysed in terms of stochastic evolution equations on domains of fractional powers of linear operators.Comment: 46 page

On multicurve models for the term structure

In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an "adjustment factor" when passing from the one-curve to the two-curve setting. The model itself corresponds to short rate modeling where the short rate and a short rate spread are driven by affine factors; this allows for correlation between short rate and short rate spread as well as to exploit the convenient affine structure methodology. We briefly comment also on the calibration of the model parameters, including the correlation factor.Comment: 16 page

Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities, an equilibrium exists and the agents' optimal trading strategies are constant. Affine processes, and the theory of information-based asset pricing are used to model the endogenous asset price dynamics and the terminal payoff. The derived semi-explicit pricing formulae are applied to numerically analyze the impact of the agents' risk aversion on the implied volatility of simultaneously-traded European-style options.Comment: 24 pages, 4 figure

Surface diffusion of Au on Si(111): A microscopic study

The direct evolution of submonolayer two-dimensional Au phases on the Si(111)-(7x7) surface was studied in real time using the spectroscopic photoemission and low energy electron microscope located at the synchrotron radiation source ELETTRA. A finite area covered by 1 monolayer (ML) of gold with a steplike transition zone was prepared by evaporation in situ. Subsequent annealing resulted in the spread of the Au layer and the formation of laterally extended Si(111)-(5x1)-Au and Si(111)-(√3x √3)R30°-Au surface reconstructions. At a temperature around 970 K, the boundary of the gold-covered region propagates on the clean Si(111)-(7x7) and exhibits a nonlinear dependence on time. The ordered Si(111)-(5x1)-Au plateau develops a separated front moving with constant velocity. Two values of the Au diffusion coefficients were estimated at a temperature of about 985 K: (1) D7x7=5,2x10-8 cm2 s-1 as the average diffusion coefficient for Au on a clean Si(111)-(7x7) surface in the concentration range from 0.4 ML up to 0.66 ML and (2) D5x1=1.2x10-7 cm2 s-1 as the lower limit for the diffusion of single Au atoms on the Si(111)-(5x1)-Au ordered phase

On the Neutralino as Dark Matter Candidate - II. Direct Detection

Evaluations of the event rates relevant to direct search for dark matter neutralino are presented for a wide range of neutralino masses and for various detector materials of preeminent interest. Differential and total rates are appropriately weighted over the local neutralino density expected on theoretical grounds.Comment: (18 pages plain TeX, 24 figures not included, available from the authors) DFTT-38/9

Evidence of vectorial photoelectric effect on Copper

Quantum Efficiency (QE) measurements of single photon photoemission from a Cu(111) single crystal and a Cu polycrystal photocathodes, irradiated by 150 fs-6.28 eV laser pulses, are reported over a broad range of incidence angle, both in s and p polarizations. The maximum QE (\simeq 4\times10^{-4}) for polycrystalline Cu is obtained in p polarization at an angle of incidence {\theta} = 65deg. We observe a QE enhancement in p polarization which can not be explained in terms of optical absorption, a phenomenon known as vectorial photoelectric effect. Issues concerning surface roughness and symmetry considerations are addressed. An explanation in terms of non local conductivity tensor is proposed.Comment: 3 pages, 3 figure

On small-noise equations with degenerate limiting system arising from volatility models

The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving instances of this equation, based on a careful implementation of saddle-point methods and (essentially) the explicit knowledge of Fourier transforms. Recent research on tail asymptotics for heat kernels [J-D. Deuschel, P.~Friz, A.~Jacquier, and S.~Violante. Marginal density expansions for diffusions and stochastic volatility, part II: Applications. 2013, arxiv:1305.6765] suggests to work with the rescaled variable $X^{\varepsilon}:=\varepsilon^{1/(1-\gamma)} X$: while allowing to turn a space asymptotic problem into a small-$\varepsilon$ problem with fixed terminal point, the process $X^{\varepsilon}$ satisfies a SDE in Wentzell--Freidlin form (i.e. with driving noise $\varepsilon dB$). We prove a pathwise large deviation principle for the process $X^{\varepsilon}$ as $\varepsilon \to 0$. As it will become clear, the limiting ODE governing the large deviations admits infinitely many solutions, a non-standard situation in the Wentzell--Freidlin theory. As for applications, the $\varepsilon$-scaling allows to derive exact log-asymptotics for path functionals of the process: while on the one hand the resulting formulae are confirmed by the CIR-CEV benchmarks, on the other hand the large deviation approach (i) applies to equations with a more general drift term and (ii) potentially opens the way to heat kernel analysis for higher-dimensional diffusions involving such an SDE as a component.Comment: 21 pages, 1 figur