Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

General Relativistic Dynamics of Irrotational Dust: Cosmological Implications

The non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.Comment: 12 pages , DFPD 93/A/6

Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second order perturbations in cosmology, assuming a flat Robertson-Walker background, giving explicit second order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.Comment: slightly revised version, accepted for publication in Classical and Quantum Gravity. 27 pages including 4 figures, latex using 2 CQG style files: ioplppt.sty, iopl10.st

Depression and conservative surgery for breast cancer

BACKGROUND: Depression is prevalent among women and associated with reduced quality of life, and therefore it is important to determine its incidence in adult women, especially in those with breast cancer. OBJECTIVE: To determine the occurrence of depression in women who underwent conservative surgery for breast cancer with or without breast reconstruction. METHODS: Seventy-five women aged between 18 and 65 years were enrolled. Patients had undergone conservative surgery for breast cancer with immediate breast reconstruction (n = 25) or without breast reconstruction (n = 25) at least one year before the study. The control group consisted of 25 women without cancer, but of similar age and educational level distribution as the other two groups. The Beck Depression Inventory was used to measure depression. The collected data were assessed using analysis of variance and the χ2 test. RESULTS: There were no significant differences between groups in age (p = 0.72) or educational level (p = 0.20). A smaller number of patients had undergone the menopause (p = 0.02) in the control group than in other groups. There were no significant differences in occurrence of depression between groups (χ2=9.97; p = 0.126). CONCLUSÍON: Conservative surgery for breast cancer did not affect the occurrence of depression in women, regardless of whether breast reconstruction was performed

Yellow fever vaccine viremia following ablative BM suppression in AML

Univ São Paulo, Sch Med, Dept Infect & Parasit Dis, São Paulo, BrazilHosp Sirio Libanes, São Paulo, BrazilUniv São Paulo, Sch Med, Div Clin Immunol & Allergy, São Paulo, BrazilFundacao Prosangue Hemoctr São Paulo, São Paulo, BrazilUniversidade Federal de São Paulo, Infect Dis Div DIPA, São Paulo, BrazilFundacao Oswaldo Cruz, Rio de Janeiro, BrazilUniversidade Federal de São Paulo, Infect Dis Div DIPA, São Paulo, BrazilWeb of Scienc

Cosmic Microwave Background anisotropies from second order gravitational perturbations

This paper presents a complete analysis of the effects of second order gravitational perturbations on Cosmic Microwave Background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collision-less fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyse the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations, that is known to give a few percent contribution to the anisotropies at small angular scales.Comment: 15 pages, revtex, no figures. Version to be published in Phys. Rev.

Signatures of Primordial non-Gaussianities in the Matter Power-Spectrum and Bispectrum: the Time-RG Approach

We apply the time-renormalization group approach to study the effect of primordial non-Gaussianities in the non-linear evolution of cosmological dark matter density perturbations. This method improves the standard perturbation approach by solving renormalization group-like equations governing the dynamics of gravitational instability. The primordial bispectra constructed from the dark matter density contrast and the velocity fields represent initial conditions for the renormalization group flow. We consider local, equilateral and folded shapes for the initial non-Gaussianity and analyze as well the case in which the non-linear parameter f_{NL} parametrizing the strength of the non-Gaussianity depends on the momenta in Fourier space through a power-law relation, the so-called running non-Gaussianity. For the local model of non-Gaussianity we compare our findings for the power-spectrum with those of recent N-body simulations and find that they accurately fit the N-body data up to wave-numbers k \sim 0.25 h/Mpc at z=0. We also present predictions for the (reduced) matter bispectra for the various shapes of non-Gaussianity.Comment: 27 pages, 12 figures. Results and discussion for a particular case added. One figure and one reference added. Matches with the version accepted for publication in the JCAP

Relativistic effects and primordial non-Gaussianity in the galaxy bias

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.Comment: 12 pages, LaTeX file; version accepted for publication in JCA

A device-independent approach to evaluate the heating performance during magnetic hyperthermia experiments: peak analysis and zigzag protocol

Accurate knowledge of the heating performance of magnetic nanoparticles (MNPs) under AC fields is critical for the development of hyperthermia-mediated applications. Usually reported in terms of the specific loss power (SLP) obtained from the temperature variation ($\Delta{T}$) vs. time (t) curve, such estimate is subjected to a huge uncertainty. Thus, very different SLP values are reported for the same particles when measured on different equipment/laboratories. This lack of control clearly hampers the further development of MNP-mediated heat-triggered technologies. Here we report a device-independent approach to calculate the SLP value of a suspension of MNPs: the SLP is obtained from the analysis of the peak at the field on/off switch of the $\Delta{T}(t)$ curve. The measurement procedure, which itself constitutes a change of paradigm within the field, is based on fundamental physics considerations: specifically to guarantee the applicability of Newton's law of cooling, as i) it corresponds to the ideal scenario in which the temperature profiles of the system during heating and cooling are the same; and ii) it diminishes the role of coexistence of various heat dissipation channels. Such an approach is supported by theoretical and computational calculations to increase the reliability and reproducibility of SLP determination. This is experimentally confirmed, demonstrating a reduction in SLP variation across 3 different devices located in 3 different laboratories. Furthermore, the application of this peak analysis method (PAM) to a rapid succession of field on/off switches that result in a zigzag-like $\Delta{T}(t)$, which we term the zigzag protocol, allows evaluating possible variations of the SLP values with time or temperature.Comment: main text: 30 pages, 9 figure