2,175 research outputs found
Massive pericardial effusion caused by hypothyroidism.
Although mild pericardial effusion is a usual finding in patients with hypothyroidism, massive pericardial effusion or pericardial tamponade is rare and customarily related to severe hypothyroidism. The diagnosis of hypothyroidism should be considered in the differential of patients presenting with unexplained pericardial effusion, even when signs and symptoms of hypothyroidism are nonexistent.info:eu-repo/semantics/publishedVersio
Lacunary generating functions of Hermite polynomials and symbolic methods
We employ an umbral formalism to reformulate the theory of Hermite polynomials and the derivation of the associated lacunary generating functions
Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities
We present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes
Hilbert transform, spectral filters and option pricing
We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (Math Finance 18(3):337–384, 2008) and Fusai et al. (Eur J Oper Res 251(4):124–134, 2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Lévy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering
Fluctuation identities with continuous monitoring and their application to the pricing of barrier options
We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener–Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-z domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme
Leray and LANS- modeling of turbulent mixing
Mathematical regularisation of the nonlinear terms in the Navier-Stokes
equations provides a systematic approach to deriving subgrid closures for
numerical simulations of turbulent flow. By construction, these subgrid
closures imply existence and uniqueness of strong solutions to the
corresponding modelled system of equations. We will consider the large eddy
interpretation of two such mathematical regularisation principles, i.e., Leray
and LANS regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS principle extends the Leray formulation in a
natural way in which a {\bfi filtered Kelvin circulation theorem},
incorporating the smoothed transport velocity, is explicitly satisfied. These
regularisation principles give rise to implied subgrid closures which will be
applied in large eddy simulation of turbulent mixing. Comparison with filtered
direct numerical simulation data, and with predictions obtained from popular
dynamic eddy-viscosity modelling, shows that these mathematical regularisation
models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure
Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
We present a numerical method for the Monte Carlo simulation of uncoupled
continuous-time random walks with a Levy alpha-stable distribution of jumps in
space and a Mittag-Leffler distribution of waiting times, and apply it to the
stochastic solution of the Cauchy problem for a partial differential equation
with fractional derivatives both in space and in time. The one-parameter
Mittag-Leffler function is the natural survival probability leading to
time-fractional diffusion equations. Transformation methods for Mittag-Leffler
random variables were found later than the well-known transformation method by
Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far
have not received as much attention; nor have they been used together with the
latter in spite of their mathematical relationship due to the geometric
stability of the Mittag-Leffler distribution. Combining the two methods, we
obtain an accurate approximation of space- and time-fractional diffusion
processes almost as easy and fast to compute as for standard diffusion
processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing
in Economics and Finance in Montreal, 14-16 June 2007; at the conference
"Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March
2008; et
Preparation for action: Psychophysiological activity preceding a motor skill as a function of expertise, performance outcome, and psychological pressure
Knowledge of the psychophysiological responses that characterize optimal motor performance is required to inform biofeedback interventions. This experiment compared cortical, cardiac, muscular, and kinematic activity in 10 experts and 10 novices as they performed golf putts in low- and high-pressure conditions. Results revealed that in the final seconds preceding movement, experts displayed a greater reduction in heart rate and EEG theta, high-alpha, and beta power, when compared to novices. EEG high-alpha power also predicted success, with participants producing less high-alpha power in the seconds preceding putts that were holed compared to those that were missed. Increased pressure had little impact on psychophysiological activity. It was concluded that greater reductions in EEG high-alpha power during preparation for action reflect more resources being devoted to response programming, and could underlie successful accuracy-based performance
Subordination Pathways to Fractional Diffusion
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and
under power law regime is splitted into three distinct random walks: (rw_1), a
random walk along the line of natural time, happening in operational time;
(rw_2), a random walk along the line of space, happening in operational
time;(rw_3), the inversion of (rw_1), namely a random walk along the line of
operational time, happening in natural time. Via the general integral equation
of CTRW and appropriate rescaling, the transition to the diffusion limit is
carried out for each of these three random walks. Combining the limits of
(rw_1) and (rw_2) we get the method of parametric subordination for generating
particle paths, whereas combination of (rw_2) and (rw_3) yields the
subordination integral for the sojourn probability density in space-time
fractional diffusion.Comment: 20 pages, 4 figure
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