Chebyshev Interpolation for Parametric Option Pricing

Function approximation with Chebyshev polynomials is a well-established and thoroughly investigated method within the field of numerical analysis. The method enjoys attractive convergence properties and its implementation is straightforward. We propose to apply tensorized Chebyshev interpolation to computing Parametric Option Prices (POP). This allows us to exploit the recurrent nature of the pricing problem in an efficient, reliable and general way. For a large variety of option types and affine asset models we prove that the convergence rate of the method is exponential if there is a single varying parameter and of any arbitrary polynomial order in the multivariate case. Numerical experiments confirm these findings and show that the method achieves a significant gain in efficiency

Quantum general covariance

The structure of quantum interactions with fields of helicity two ("gravitons") is strongly constrained by three principles: positivity (Hilbert space), covariance, and locality of observables. To fulfil them simultaneously, some (non-observable) fields need to be non-local. We work with string-localized fields. The results then follow from the condition that entities closely related to observables, like the S-matrix, be local and string-independent. They in particular reproduce the interactions dictated by general covariance in classical field theory. Graviton-matter couplings are consistent only when the graviton self-interaction is taken into account as well.Comment: 36 pages. v2: 38 pages, Dirac coupling case included, otherwise as to appear in Class. Qu. Gra

Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models

Two essential quantities for the analysis of approximation schemes of evolution equa- tions are stability and convergence. We derive stability and convergence of fully discrete approximation schemes of solutions to linear parabolic evolution equations governed by time dependent coercive operators. We consider abstract Galerkin ap- proximations in space combined with theta-schemes in time. The level of generality of our analysis comprises both a large class of time-dependent operators and a large choice of approximating Galerkin spaces. In particular the results apply to partial integro differential equations for option pricing in time-inhomogeneous Lévy models and allows for a large variety of option types and models. The derivation builds on the strong foundation laid out by von Petersdorff and Schwab (2003) who provide the respective results for the time-homogeneous case. We discuss the assumptions in the context of option pricing

Revisiting the Okubo–Marshak Argument

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo–Marshak argument on the non-existence of a “strong CP problem” in quantum chromodynamics

Chemical Aspects of the Candidate Antiferromagnetic Topological Insulator MnBi₂Te₄

High-quality single crystals of MnBi 2 Te 4 are grown for the first time by slow cooling within a narrow range between the melting points of Bi 2 Te 3 (586 °C) and MnBi 2 Te 4 (600 °C). Single-crystal X-ray diffraction and electron microscopy reveal ubiquitous antisite defects in both cation sites and, possibly, Mn vacancies (Mn 0.85(3) Bi 2.10(3) Te 4 ). Thermochemical studies complemented with high-temperature X-ray diffraction establish a limited high-temperature range of phase stability and metastability at room temperature. Nevertheless, the synthesis of MnBi 2 Te 4 can be scaled-up as powders can be obtained at subsolidus temperatures and quenched at room temperature. Bulk samples exhibit long-range antiferromagnetic ordering below 24 K. The Mn(II) out-of-plane magnetic state is confirmed by the magnetization, X-ray photoemission, X-ray absorption, and linear dichroism measurements. The compound shows a metallic type of resistivity in the range 4.5-300 K and is an n-type conductor that reaches a thermoelectric figure of merit up to ZT = 0.17. Angle-resolved photoemission experiments show a surface state forming a gapped Dirac cone, thus strengthening MnBi 2 Te 4 as a promising candidate for the intrinsic magnetic topological insulator, in accordance with theoretical predictions. The developed synthetic protocols enable further experimental studies of a crossover between magnetic ordering and nontrivial topology in bulk MnBi 2 Te 4 . © 2019 American Chemical Society

Indications and Route of Hysterectomy for Benign Diseases. Guideline of the DGGG, OEGGG and SGGG (S3 Level, AWMF Registry No. 015/070, April 2015)

Background: Official guideline "indications and methods of hysterectomy" to assign indications for the different methods published and coordinated by the German Society of Gynecology and Obstetrics (DGGG), the Austrian Society of Gynecology and Obstetrics (OEGGG) and the Swiss Society of Gynecology and Obstetrics (SGGG). Besides vaginal and abdominal hysterectomy, three additional techniques have been implemented due to the introduction of laparoscopy. Organ-sparing alternatives were also integrated. Methods: The guideline group consisted of 26 experts from Germany, Austria and Switzerland. Recommendations were developed using a structured consensus process and independent moderation. A systematic literature search and quality appraisal of benefits and harms of the therapeutic alternatives for symptomatic fibroids, dysfunctional bleeding and adenomyosis was done through MEDLINE up to 6/2014 focusing on systematic reviews and meta-analysis. Results: All types of hysterectomy led in studies to high rates of patient satisfaction. If possible, vaginal instead of abdominal hysterectomy should preferably be done. If a vaginal hysterectomy is not feasible, the possibility of a laparoscopic hysterectomy should be considered. An abdominal hysterectomy should only be done with a special indication. Organ-sparing interventions also led to high patient satisfaction rates, but contain the risk of symptom recurrence. Conclusion: As an aim, patients should be enabled to choose that therapeutic intervention for their benign disease of the uterus that convenes best to them and their personal life situation