On multigrid for anisotropic equations and variational inequalities: pricing multi-dimensional European and American options

Partial differential operators in finance often originate in bounded linear stochastic processes. As a consequence, diffusion over these boundaries is zero and the corresponding coefficients vanish. The choice of parameters and stretched grids lead to additional anisotropies in the discrete equations or inequalities. In this study various block smoothers are tested in numerical experiments for equations of Black–Scholes-type (European options) in several dimensions. For linear complementarity problems, as they arise from optimal stopping time problems (American options), the choice of grid transfer is also crucial to preserve complementarity conditions on all grid levels. We adapt the transfer operators at the free boundary in a suitable way and compare with other strategies including cascadic approaches and full approximation schemes

Efficient hierarchical approximation of high-dimensional option pricing problems

A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretisation can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted

The Effects of Surgical Masks on Speech Perception in Noise

Surgical masks and blood shields worn by anesthesiologists and surgeons in hospital operating rooms may negatively impact speech communication and put patients at risk. Young adult subjects listened to sentences from the Speech Perception in Noise test, SPIN, (Bilger et al., 1984) recorded by a male and female talker. All eight SPIN lists were recorded under three different speaking conditions: 1) speaking normally without any obstruction, 2) wearing a typical surgical mask, and 3) wearing a surgical mask with an attached blood shield. Multi-talker babble was mixed with the SPIN sentences at the signal-to-noise ratio of 0 dB to simulate conversation in noisy environments. Speaker gender and recording conditions were counterbalanced across listeners to control for learning and fatigue effects. SPIN test scores for each of the three types of recordings and both talker genders were compared in order to determine the degradation that blood-shields and surgical masks may have on speech communication in the operating room. The data suggests that surgical masks, in particular the blood shields, negatively impact speech communication. Percent correct is the highest for the unmasked condition, followed by the masked condition, and poorest in the mask and attached blood shield condition.Research grant from the Division of Social and Behavioral SciencesScholarship from the College of Arts and SciencesDr. Peter Winch of Nationwide Children's HospitalDr. Jeanne Gokcen of FutureCom Technologies Inc.No embargoAcademic Major: Speech and Hearing Scienc

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

Making La Ciudad Blanca: Race, Region, and Reconstruction in Nation Building Bolivia

Prior to the 1899 Federal Revolution, Sucre elite used the memory of Chuquisaca independence exploits to justify their rule and imagine a future for the Bolivian nation. These symbols became widespread in the Bolivian public sphere and were the dominant national discourse for the Bolivian nation. However, dissatisfied highland elite began crafting an alternative national project and these two competing Nationalisms clashed and eventually led to the 1899 Federal Revolution. Following the war, the Liberal Party allowed and even supported a continuation of the Sucre based origin story in the Valley regions of Bolivia. This has created ideas of “Sucrense exceptionalism,” the discourse has been used continually to make political demands, and it was one of the underlying causes of the 2008 act of racial violence that took place in Sucre, Bolivia

On multigrid for anisotropic equations and variational inequalities: pricing multi-dimensional European and American options

Partial differential operators in finance often originate in bounded linear stochastic processes. As a consequence, diffusion over these boundaries is zero and the corresponding coefficients vanish. The choice of parameters and stretched grids lead to additional anisotropies in the discrete equations or inequalities. In this study various block smoothers are tested in numerical experiments for equations of Black–Scholes-type (European options) in several dimensions. For linear complementarity problems, as they arise from optimal stopping time problems (American options), the choice of grid transfer is also crucial to preserve complementarity conditions on all grid levels. We adapt the transfer operators at the free boundary in a suitable way and compare with other strategies including cascadic approaches and full approximation schemes

The Chasquis of Liberty: Revolutionary Messengers in the Bolivian Independence Era, 1808-1825

This dissertation focuses on a group of South American revolutionaries and the ways they shaped and challenged the precepts of the Age of Revolutions that rocked Latin America, Europe, and the Atlantic World in the early nineteenth century. Specifically, it investigates revolutionaries like Vicente Pazos Kanki, an indigenous journalist and diplomat, who traveled throughout South America, the United States, and Europe in an effort to form republican governments that brought together indigenous, African, and European citizens into multiethnic republics. I call these revolutionaries the chasquis of liberty. A chasqui was the rapid-traveling foot messenger of the Andean preconquest and colonial worlds. I use this metaphor to illustrate the ways revolutionaries connected disparate struggles for independence and made hemispheric republicanism a reality by forming alliances with other nation states’ luminaries, like the U.S. politician Henry Clay. More than simple messengers, the chasquis of liberty envisioned an inclusive republicanism that stood in contrast to other republics in the Atlantic World that defended slavery and racial exclusion

A three-dimensional model of a gap junction

Gap junctions are effective electric couplings between neurons and form a very important way of communication between them. Since they can be considered as the points on the neuron’s membrane on which for example dendrites of different cells become one piece, in three dimensions they can be modelled by observing this property in the created geometry. Thus they can be easily made part in an already existing 3-dimensional model for signal propagation on the neuron’s membrane, if the geometries are chosen in such a way that they respect the blending of the membranes. A small network of two cells was created, which blend in their dendrites and a simulation of the three-dimensional model was carried out which reveals the fast transmission of the signal from one cell to the other

Mathematical modeling of the Drosophila neuromuscular junction

Poster presentation: An important challenge in neuroscience is understanding how networks of neurons go about processing information. Synapses are thought to play an essential role in cellular information processing however quantitative and mathematical models of the underlying physiologic processes that occur at synaptic active zones are lacking. We are generating mathematical models of synaptic vesicle dynamics at a well-characterized model synapse, the Drosophila larval neuromuscular junction. This synapse's simplicity, accessibility to various electrophysiological recording and imaging techniques, and the genetic malleability intrinsic to Drosophila system make it ideal for computational and mathematical studies. We have employed a reductionist approach and started by modeling single presynaptic boutons. Synaptic vesicles can be divided into different pools; however, a quantitative understanding of their dynamics at the Drosophila neuromuscular junction is lacking [4]. We performed biologically realistic simulations of high and low release probability boutons [3] using partial differential equations (PDE) taking into account not only the evolution in time but also the spatial structure in two dimensions (the extension to three dimensions will be implemented soon). PDEs are solved using UG, a program library for the calculation of multi-dimensional PDEs solved using a finite volume approach and implicit time stepping methods leading to extended linear equation systems be solvedwith multi-grid methods [3,4]. Numerical calculations are done on multi-processor computers for fast calculations using different parameters in order to asses the biological feasibility of different models. In preliminary simulations, we modeled vesicle dynamics as a diffusion process describing exocytosis as Neumann streams at synaptic active zones. The initial results obtained with these models are consistent with experimental data. However, this should be regarded as a work in progress. Further refinements will be implemented, including simulations using morphologically realistic geometries which were generated from confocal scans of the neuromuscular junction using NeuRA (a Neuron Reconstruction Algorithm). Other parameters such as glutamate diffusion and reuptake dynamics, as well as postsynaptic receptor kinetics will be incorporated as well