Fractional diffusion models of option prices in markets with jumps

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.     

Is Empty Spacetime a Physical Thing?

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation—as well as conceptual overthrow—of this geometric ether.     

Paradoxical vocal fold motion: Presentation and treatment options

Paradoxical vocal fold motion is a rare disorder in which adduction of the folds occurs on inspiration. The disorder presents with signs of airway obstruction and often airway distress, so proper diagnosis by the otorhinolaryngologist is critical to subsequent management. We present a retrospective review of 10 patients with the diagnosis of paradoxical vocal fold motion seen over a 6-year period. Eight patients were females, and 6 required an acute airway intervention at presentation; 3 patients eventually underwent tracheotomy for respiratory decompensation. Six patients had a prior diagnosis of asthma, and this was determined to contribute to their respiratory status. Five patients were treated with botulinum toxin and 2 with flexible nasolaryngoscopic biofeedback, which improved the outcome. A review of the literature confirms a female predominance of patients presenting with paradoxical adduction and airway distress, often with a history of asthma and psychopathology. Our experience with botulinum toxin and biofeedback suggests that these procedures are viable treatment options in the management of patients with this disorder.     

Fluorescence emission of excited hydrogen atoms after core excitation of water vapor

The Balmer emission from atomic hydrogen has been recorded across the resonances at the oxygen K edge of the water molecule using synchrotron radiation excitation. The emission is observed to be strongest at excitations to Rydberg resonances. The observations are interpreted using a qualitative model for the dynamics of the core-to-Rydberg excited molecule. The model links the quantum state of the core-excited water molecule via resonant Auger decay and subsequent dissociation to the state of the fluorescing hydrogen atom.     

Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime.     

Nucleon structure functions from high energy neutrino interactions

Structure functions obtained from high energy neutrino and antineutrino scattering from an iron target are presented. These were extracted from the combined data of Fermilab experiments E616 and E701; these utilized narrow band beam runs between 1979–1982. The structure functions are used to test the validity of quarkparton model (QPM) predictions and to extract the QCD scale parameter Λ from fits to the Altarelli-Parisi equations.     

Reply to Comment on “Towards a large deviation theory for strongly correlated systems”

The computational study commented by Touchette opens the door to a desirable generalization of standard large deviation theory for special, though ubiquitous, correlations. We focus on three inter-related aspects: (i) numerical results strongly suggest that the standard exponential probability law is asymptotically replaced by a power-law dominant term; (ii) a subdominant term appears to reinforce the thermodynamically extensive entropic nature of q-generalized rate function; (iii) the correlations we discussed, correspond to Q-Gaussian distributions, differing from Lévy?s, except in the case of Cauchy–Lorentz distributions. Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) escaped to his analysis. Claiming the absence of connection with q-exponentials is unjustified.     

The Automorphism Group of a Simple Tracially AI Algebra

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group .