Time-Changed Fast Mean-Reverting Stochastic Volatility Models

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales

Multiple indices of diffusion identifies white matter damage in mild cognitive impairment and Alzheimer's disease

The study of multiple indices of diffusion, including axial (DA), radial (DR) and mean diffusion (MD), as well as fractional anisotropy (FA), enables WM damage in Alzheimer's disease (AD) to be assessed in detail. Here, tract-based spatial statistics (TBSS) were performed on scans of 40 healthy elders, 19 non-amnestic MCI (MCIna) subjects, 14 amnestic MCI (MCIa) subjects and 9 AD patients. Significantly higher DA was found in MCIna subjects compared to healthy elders in the right posterior cingulum/precuneus. Significantly higher DA was also found in MCIa subjects compared to healthy elders in the left prefrontal cortex, particularly in the forceps minor and uncinate fasciculus. In the MCIa versus MCIna comparison, significantly higher DA was found in large areas of the left prefrontal cortex. For AD patients, the overlap of FA and DR changes and the overlap of FA and MD changes were seen in temporal, parietal and frontal lobes, as well as the corpus callosum and fornix. Analysis of differences between the AD versus MCIna, and AD versus MCIa contrasts, highlighted regions that are increasingly compromised in more severe disease stages. Microstructural damage independent of gross tissue loss was widespread in later disease stages. Our findings suggest a scheme where WM damage begins in the core memory network of the temporal lobe, cingulum and prefrontal regions, and spreads beyond these regions in later stages. DA and MD indices were most sensitive at detecting early changes in MCIa

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Sensitivity and Specificity of Multiple Kato-Katz Thick Smears and a Circulating Cathodic Antigen Test for Schistosoma mansoni Diagnosis Pre- and Post-repeated-Praziquantel Treatment

Two Kato-Katz thick smears (Kato-Katzs) from a single stool are currently recommended for diagnosing Schistosoma mansoni infections to map areas for intervention. This ‘gold standard’ has low sensitivity at low infection intensities. The urine point-of-care circulating cathodic antigen test (POC-CCA) is potentially more sensitive but how accurately they detect S. mansoni after repeated praziquantel treatments, their suitability for measuring drug efficacy and their correlation with egg counts remain to be fully understood. We compared the accuracies of one to six Kato-Katzs and one POC-CCA for the diagnosis of S. mansoni in primary-school children who have received zero to ten praziquantel treatments. We determined the impact each diagnostic approach may have on monitoring and evaluation (M&E) and drug-efficacy findings

Multi-parallel qPCR provides increased sensitivity and diagnostic breadth for gastrointestinal parasites of humans: field-based inferences on the impact of mass deworming

BACKGROUND: Although chronic morbidity in humans from soil transmitted helminth (STH) infections can be reduced by anthelmintic treatment, inconsistent diagnostic tools make it difficult to reliably measure the impact of deworming programs and often miss light helminth infections. METHODS: Cryopreserved stool samples from 796 people (aged 2-81 years) in four villages in Bungoma County, western Kenya, were assessed using multi-parallel qPCR for 8 parasites and compared to point-of-contact assessments of the same stools by the 2-stool 2-slide Kato-Katz (KK) method. All subjects were treated with albendazole and all Ascaris lumbricoides expelled post-treatment were collected. Three months later, samples from 633 of these people were re-assessed by both qPCR and KK, re-treated with albendazole and the expelled worms collected. RESULTS: Baseline prevalence by qPCR (n = 796) was 17 % for A. lumbricoides, 18 % for Necator americanus, 41 % for Giardia lamblia and 15% for Entamoeba histolytica. The prevalence was <1% for Trichuris trichiura, Ancylostoma duodenale, Strongyloides stercoralis and Cryptosporidium parvum. The sensitivity of qPCR was 98% for A. lumbricoides and N. americanus, whereas KK sensitivity was 70% and 32%, respectively. Furthermore, qPCR detected infections with T. trichiura and S. stercoralis that were missed by KK, and infections with G. lamblia and E. histolytica that cannot be detected by KK. Infection intensities measured by qPCR and by KK were correlated for A. lumbricoides (r = 0.83, p < 0.0001) and N. americanus (r = 0.55, p < 0.0001). The number of A. lumbricoides worms expelled was correlated (p < 0.0001) with both the KK (r = 0.63) and qPCR intensity measurements (r = 0.60). CONCLUSIONS: KK may be an inadequate tool for stool-based surveillance in areas where hookworm or Strongyloides are common or where intensity of helminth infection is low after repeated rounds of chemotherapy. Because deworming programs need to distinguish between populations where parasitic infection is controlled and those where further treatment is required, multi-parallel qPCR (or similar high throughput molecular diagnostics) may provide new and important diagnostic information

General optimized lower and upper bounds for discrete and continuous arithmetic Asian options

We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

New approaches to measuring anthelminthic drug efficacy: parasitological responses of childhood schistosome infections to treatment with praziquantel

By 2020, the global health community aims to control and eliminate human helminthiases, including schistosomiasis in selected African countries, principally by preventive chemotherapy (PCT) through mass drug administration (MDA) of anthelminthics. Quantitative monitoring of anthelminthic responses is crucial for promptly detecting changes in efficacy, potentially indicative of emerging drug resistance. Statistical models offer a powerful means to delineate and compare efficacy among individuals, among groups of individuals and among populations.; We illustrate a variety of statistical frameworks that offer different levels of inference by analysing data from nine previous studies on egg counts collected from African children before and after administration of praziquantel.; We quantify responses to praziquantel as egg reduction rates (ERRs), using different frameworks to estimate ERRs among population strata, as average responses, and within strata, as individual responses. We compare our model-based average ERRs to corresponding model-free estimates, using as reference the World Health Organization (WHO) 90 % threshold of optimal efficacy. We estimate distributions of individual responses and summarize the variation among these responses as the fraction of ERRs falling below the WHO threshold.; Generic models for evaluating responses to anthelminthics deepen our understanding of variation among populations, sub-populations and individuals. We discuss the future application of statistical modelling approaches for monitoring and evaluation of PCT programmes targeting human helminthiases in the context of the WHO 2020 control and elimination goals