Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time $t_d$ during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of $t_d$, and tends to $0$ as time tends to $t_d^-$ with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of $t_d$. When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.

Microbubble formation and pinch-off scaling exponent in flow-focusing devices

We investigate the gas jet breakup and the resulting microbubble formation in a microfluidic flow-focusing device using ultra high-speed imaging at 1 million frames/s. In recent experiments [Dollet et al., Phys. Rev. Lett. 100, 034504 (2008)] it was found that in the final stage of the collapse the radius of the neck scales with time with a 1/3 power-law exponent, which suggested that gas inertia and the Bernoulli suction effect become important. Here, ultra high-speed imaging was used to capture the complete bubble contour and quantify the gas flow through the neck. It revealed that the resulting decrease in pressure, due to Bernoulli suction, is too low to account for an accelerated pinch-off. The high temporal resolution images enable us to approach the final moment of pinch-off to within 1 {\mu}s. We observe that the final moment of bubble pinch-off is characterized by a scaling exponent of 0.41 +/- 0.01. This exponent is approximately 2/5, which can be derived, based on the observation that during the collapse the neck becomes less slender, due to the exclusive driving through liquid inertia

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps

Local optical field variation in the neighborhood of a semiconductor micrograting

The local optical field of a semiconductor micrograting (GaAs, 10x10 micro m) is recorded in the middle field region using an optical scanning probe in collection mode at constant height. The recorded image shows the micro-grating with high contrast and a displaced diffraction image. The finite penetration depth of the light leads to a reduced edge resolution in the direction to the illuminating beam direction while the edge contrast in perpendicular direction remains high (~100nm). We use the discrete dipole model to calculate the local optical field to show how the displacement of the diffraction image increases with increasing distance from the surface.Comment: 12 pages, 3 figure

Fly eyes are not still: a motion illusion in Drosophila flight supports parallel visual processing.

Most animals shift gaze by a 'fixate and saccade' strategy, where the fixation phase stabilizes background motion. A logical prerequisite for robust detection and tracking of moving foreground objects, therefore, is to suppress the perception of background motion. In a virtual reality magnetic tether system enabling free yaw movement, Drosophila implemented a fixate and saccade strategy in the presence of a static panorama. When the spatial wavelength of a vertical grating was below the Nyquist wavelength of the compound eyes, flies drifted continuously and gaze could not be maintained at a single location. Because the drift occurs from a motionless stimulus - thus any perceived motion stimuli are generated by the fly itself - it is illusory, driven by perceptual aliasing. Notably, the drift speed was significantly faster than under a uniform panorama, suggesting perceptual enhancement as a result of aliasing. Under the same visual conditions in a rigid-tether paradigm, wing steering responses to the unresolvable static panorama were not distinguishable from those to a resolvable static pattern, suggesting visual aliasing is induced by ego motion. We hypothesized that obstructing the control of gaze fixation also disrupts detection and tracking of objects. Using the illusory motion stimulus, we show that magnetically tethered Drosophila track objects robustly in flight even when gaze is not fixated as flies continuously drift. Taken together, our study provides further support for parallel visual motion processing and reveals the critical influence of body motion on visuomotor processing. Motion illusions can reveal important shared principles of information processing across taxa

Doubly-charged particles at the Large Hadron Collider

In this work we investigate the production and signatures of doubly-charged particles at the Large Hadron Collider. We start with the Standard Model particle content and representations and add generic doubly-charged exotic particles. We classify these doubly-charged states according to their spin, considering scalar, fermionic and vectorial fields, and according to their SU(2)L representation, being chosen to be either trivial, fundamental, or adjoint. We write the most general interactions between them and the Standard Model sector and study their production modes and possible decay channels. We then probe how they can most likely be observed and how particles with different spin and SU(2)L representations could be possibly distinguished.Comment: 18 pages, 8 figures, 1 table; version accepted by Phys.Rev.

Role of the Channel Geometry on the Bubble Pinch-Off in Flow-Focusing Devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling wm~tau1/3 between the neck width wm and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity

Automated mass spectrum generation for new physics

We describe an extension of the FeynRules package dedicated to the automatic generation of the mass spectrum associated with any Lagrangian-based quantum field theory. After introducing a simplified way to implement particle mixings, we present a new class of FeynRules functions allowing both for the analytical computation of all the model mass matrices and for the generation of a C++ package, dubbed ASperGe. This program can then be further employed for a numerical evaluation of the rotation matrices necessary to diagonalize the field basis. We illustrate these features in the context of the Two-Higgs-Doublet Model, the Minimal Left-Right Symmetric Standard Model and the Minimal Supersymmetric Standard Model.Comment: 11 pages, 1 table; version accepted by EPJ

Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects

The Tb$_2$Ti$_2$O$_7$ pyrochlore magnetic material is attracting much attention for its {\em spin liquid} state, failing to develop long range order down to 50 mK despite a Curie-Weiss temperature $\theta_{\rm CW} \sim -14$ K. In this paper we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low temperature properties. The naturally-tuned proximity of this system near a N\'eel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low energy spin Hamiltonian. As a result, Tb$_2$Ti$_2$O$_7$ is argued to be a {\em quantum spin ice}. We put forward an experimental test of this proposal using neutron scattering on a single crystal.Comment: 5 pages, 3 figures. Version 2 has a modified introduction. Figure 2b of version 1 (experimental neutron scattering has been removed. A proposal for an experimental test is now included accompanied by a new Figure (Fig. 3