The wiener-hopf technique and discretely monitored path-dependent option pricing

Fusai, Abrahams, and Sgarra (2006) employed the Wiener-Hopf technique to obtain an exact analytic expression for discretely monitored barrier option prices as the solution to the Black-Scholes partial differential equation. The present work reformulates this in the language of random walks and extends it to price a variety of other discretely monitored path-dependent options. Analytic arguments familiar in the applied mathematics literature are used to obtain fluctuation identities. This includes casting the famous identities of Baxter and Spitzer in a form convenient to price barrier, first-touch, and hindsight options. Analyzing random walks killed by two absorbing barriers with a modified Wiener-Hopf technique yields a novel formula for double-barrier option prices. Continuum limits and continuity correction approximations are considered. Numerically, efficient results are obtained by implementing Padé approximation. A Gaussian Black-Scholes framework is used as a simple model to exemplify the techniques, but the analysis applies to Lévy processes generally

Galerkin Method in the Gravitational Collapse: a Dynamical System Approach

We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary differential equations for modal coefficients, after a convenient truncation procedure, largely applied to problems of turbulence. In the present case, we have generated a finite dynamical system that reproduces the essential features of the dynamics of the gravitational collapse, even for a lower order of truncation. Each initial condition in the space of modal coefficients corresponds to a well definite spatial distribution of scalar field. Numerical experiments with the dynamical system show that depending on the strength of the scalar field packet, the formation of black-holes or the dispersion of the scalar field leaving behind flat spacetime are the two main outcomes. We also found numerical evidence that between both asymptotic states, there is a critical solution represented by a limit cycle in the modal space with period $\Delta u \approx 3.55$.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres

Anderson localization of matter waves in tailored disordered potentials

We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy increases, for appropriately tailored disorder correlations. We predict the effect in one, two, and three dimensions, and propose a simple method to observe it using ultracold atoms placed in optical disorder. The increase of localization with the particle energy can serve to discriminate quantum versus classical localization

Sjögren's and plasma cell variant Castleman disease: a case report

Castleman disease is a rare cause of lymphoid hyperplasia and may result in localized symptoms or an aggressive, multisystem disorder. It can mimic other diseases like lymphoma or tuberculosis. It classically presents as a mediastinal mass that involves the lymphatic tissue primarily but can also affect extra lymphatic sites including the lungs, larynx, parotid glands, pancreas, meninges, and muscles. In HIV and HHV8-negative patients with idiopathic multicentric Castleman disease, pathogenesis may involve autoimmune mechanisms. We highlight and report a case of a 34-year-old Ghanaian female who was successfully diagnosed and managed for Sjögren's as well as plasma cell variant Castleman disease with combination chemotherapy and rituximab followed by eighteen months maintenance therapy with pulse chlorambucil and prednisolone and three monthly rituximab.Keywords: lymphadenopathy, chemotherapy, Rituximab, Plasma Cell Variant Castleman Disease, Sjögren's syndrom

Topochemical transformation of two-dimensional single crystalline Na0.5Bi0.5TiO3-BaTiO3 platelets from Na0.5Bi4.5Ti4O15 precursors and their piezoelectricity

This work was financially supported by the Defence Industrial Technology Development Program, China (grant no. A1420133028) the Natural Science Foundation of China (grant no: 51072235), Hunan Nonferrous Research Funding (grant no: YSZN2013CL05), Hunan Doctoral Research Innovation Project (grant no: CX2014B055) and China Scholarship Council (grant no: 201506370175)

Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point is splitted into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990). The possibility of restoring the conventional picture still exists but requires a radical reinterpretetion of the raw numerical data.Comment: PDF, 11 page

Statistics of quantum transmission in one dimension with broad disorder

We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the logarithm of the transmission probability through this unit. Unit actions and lengths are independent random variables, with a common distribution that is either narrow or broad. This investigation is motivated by results on disordered systems with non-stationary random potentials whose fluctuations grow with distance. In the statistical ensemble at fixed total sample length four phases can be distinguished, according to the values of the indices characterizing the distribution of the unit actions and lengths. The sample action, which is proportional to the logarithm of the conductance across the sample, is found to obey a fluctuating scaling law, and therefore to be non-self-averaging, in three of the four phases. According to the values of the two above mentioned indices, the sample action may typically grow less rapidly than linearly with the sample length (underlocalization), more rapidly than linearly (superlocalization), or linearly but with non-trivial sample-to-sample fluctuations (fluctuating localization).Comment: 26 pages, 4 figures, 1 tabl

Mesoporous Strontium-Doped Phosphate-Based Sol-Gel Glasses for Biomedical Applications

Mesoporous phosphate-based glasses have great potential as biomedical materials being able to simultaneously induce tissue regeneration and controlled release of therapeutic molecules. In the present study, a series of mesoporous phosphate-based glasses in the P2O5-CaO-Na2O system doped with 1, 3, and 5 mol % of Sr2+ were prepared using the sol-gel method combined with supramolecular templating. A sample without strontium addition was prepared for comparison. The non-ionic triblock copolymer EO20PO70EO20 (P123) was used as a templating agent. SEM images revealed that all synthesized glasses have an extended porous structure. This was confirmed by N2 adsorption-desorption analysis at 77 K that shows a porosity typical of mesoporous materials. 31P magic angle spinning nuclear magnetic resonance (31P MAS-NMR) and Fourier transform infrared (FTIR) spectroscopies have shown that the glasses are mainly formed by Q1 and Q2 phosphate groups. Degradation of the glasses in deionized water assessed over a 7-day period shows that phosphate, Ca2+, Na+ and Sr2+ ions can be released in a controlled matter over time. In particular, a direct correlation between strontium content and degradation rate was observed. This study shows that Sr-doped mesoporous phosphate-based glasses have great potential in bone tissue regeneration as materials for controlled delivery of therapeutic ions