Alpha-root Processes for Derivatives pricing

A class of mean reverting positive stochastic processes driven by alpha-stable distributions are discussed. A subclass of affine processes, they are referred to here as alpha-root processes in analogy to the square root process or the Cox-Ingersoll-Ross process derived from the Brownian motion. Being affine, they provide semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Their use has not been appreciated in the field perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a formulation that admits an efficient simulation algorithm to enable an extensive investigation of their properties

Alpha-root Processes for Derivatives pricing

A class of mean reverting positive stochastic processes driven by alpha-stable distributions, 1<=alpha<2, are discussed. They are referred to as alpha-root processes in analogy to the square root process or the Cox-Ingersoll-Ross process derived from the Brownian motion. They are affine models in the same sense as the square root process, providing semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Though likely that they have caught the attention of researchers in the field, their use has not been appreciated perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a formulation that admits an efficient simulation algorithm to enable an extensive investigation of their properties

Alpha-root Processes for Derivatives pricing

A class of mean reverting positive stochastic processes driven by alpha-stable distributions, referred to here as alpha-root processes in analogy to the square root process (Cox-Ingersoll-Ross process), is a subclass of affine processes, in particular continuous state branching processes with immigration (CBI processes). Being affine, they provide semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Their use has not been appreciated in the field perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a convenient formulation of such processes, CBI processes in general, in the form of pure-jump processes of infinite activity. The formulation admits an efficient simulation algorithm that enables an extensive investigation of their properties

Axion Protection from Flavor

The QCD axion fails to solve the strong CP problem unless all explicit PQ violating, Planck-suppressed, dimension n<10 operators are forbidden or have exponentially small coefficients. We show that all theories with a QCD axion contain an irreducible source of explicit PQ violation which is proportional to the determinant of the Yukawa interaction matrix of colored fermions. Generically, this contribution is of low operator dimension and will drastically destabilize the axion potential, so its suppression is a necessary condition for solving the strong CP problem. We propose a mechanism whereby the PQ symmetry is kept exact up to n=12 with the help of the very same flavor symmetries which generate the hierarchical quark masses and mixings of the SM. This "axion flavor protection" is straightforwardly realized in theories which employ radiative fermion mass generation and grand unification. A universal feature of this construction is that the heavy quark Yukawa couplings are generated at the PQ breaking scale.Comment: 16 pages, 2 figure

Worldwide trends in hypertension prevalence and progress in treatment and control from 1990 to 2019: a pooled analysis of 1201 population-representative studies with 104 million participants

Background: Hypertension can be detected at the primary health-care level and low-cost treatments can effectively control hypertension. We aimed to measure the prevalence of hypertension and progress in its detection, treatment, and control from 1990 to 2019 for 200 countries and territories.Methods: We used data from 1990 to 2019 on people aged 30-79 years from population-representative studies with measurement of blood pressure and data on blood pressure treatment. We defined hypertension as having systolic blood pressure 140 mm Hg or greater, diastolic blood pressure 90 mm Hg or greater, or taking medication for hypertension. We applied a Bayesian hierarchical model to estimate the prevalence of hypertension and the proportion of people with hypertension who had a previous diagnosis (detection), who were taking medication for hypertension (treatment), and whose hypertension was controlled to below 140/90 mm Hg (control). The model allowed for trends over time to be non-linear and to vary by age.Findings: The number of people aged 30-79 years with hypertension doubled from 1990 to 2019, from 331 (95% credible interval 306-359) million women and 317 (292-344) million men in 1990 to 626 (584-668) million women and 652 (604-698) million men in 2019, despite stable global age-standardised prevalence. In 2019, age-standardised hypertension prevalence was lowest in Canada and Peru for both men and women; in Taiwan, South Korea, Japan, and some countries in western Europe including Switzerland, Spain, and the UK for women; and in several low-income and middle-income countries such as Eritrea, Bangladesh, Ethiopia, and Solomon Islands for men. Hypertension prevalence surpassed 50% for women in two countries and men in nine countries, in central and eastern Europe, central Asia, Oceania, and Latin America. Globally, 59% (55-62) of women and 49% (46-52) of men with hypertension reported a previous diagnosis of hypertension in 2019, and 47% (43-51) of women and 38% (35-41) of men were treated. Control rates among people with hypertension in 2019 were 23% (20-27) for women and 18% (16-21) for men. In 2019, treatment and control rates were highest in South Korea, Canada, and Iceland (treatment >70%; control >50%), followed by the USA, Costa Rica, Germany, Portugal, and Taiwan. Treatment rates were less than 25% for women and less than 20% for men in Nepal, Indonesia, and some countries in sub-Saharan Africa and Oceania. Control rates were below 10% for women and men in these countries and for men in some countries in north Africa, central and south Asia, and eastern Europe. Treatment and control rates have improved in most countries since 1990, but we found little change in most countries in sub-Saharan Africa and Oceania. Improvements were largest in high-income countries, central Europe, and some upper-middle-income and recently high-income countries including Costa Rica, Taiwan, Kazakhstan, South Africa, Brazil, Chile, Turkey, and Iran.Interpretation: Improvements in the detection, treatment, and control of hypertension have varied substantially across countries, with some middle-income countries now outperforming most high-income nations. The dual approach of reducing hypertension prevalence through primary prevention and enhancing its treatment and control is achievable not only in high-income countries but also in low-income and middle-income settings.Copyright (C) 2021 World Health Organization; licensee Elsevier.</p

General and abdominal adiposity and hypertension in eight world regions: a pooled analysis of 837 population-based studies with 7•5 million participants

Background Adiposity can be measured using BMI (which is based on weight and height) as well as indices of abdominal adiposity. We examined the association between BMI and waist-to-height ratio (WHtR) within and across populations of different world regions and quantified how well these two metrics discriminate between people with and without hypertension. Methods We used data from studies carried out from 1990 to 2023 on BMI, WHtR and hypertension in people aged 20–64 years in representative samples of the general population in eight world regions. We graphically compared the regional distributions of BMI and WHtR, and calculated Pearson's correlation coefficients between BMI and WHtR within each region. We used mixed-effects linear regression to estimate the extent to which WHtR varies across regions at the same BMI. We graphically examined the prevalence of hypertension and the distribution of people who have hypertension both in relation to BMI and WHtR, and we assessed how closely BMI and WHtR discriminate between participants with and without hypertension using C-statistic and net reclassification improvement (NRI). Findings The correlation between BMI and WHtR ranged from 0·76 to 0·89 within different regions. After adjusting for age and BMI, mean WHtR was highest in south Asia for both sexes, followed by Latin America and the Caribbean and the region of central Asia, Middle East and north Africa. Mean WHtR was lowest in central and eastern Europe for both sexes, in the high-income western region for women, and in Oceania for men. Conversely, to achieve an equivalent WHtR, the BMI of the population of south Asia would need to be, on average, 2·79 kg/m2 (95% CI 2·31–3·28) lower for women and 1·28 kg/m2 (1·02–1·54) lower for men than in the high-income western region. In every region, hypertension prevalence increased with both BMI and WHtR. Models with either of these two adiposity metrics had virtually identical C-statistics and NRIs for every region and sex, with C-statistics ranging from 0·72 to 0·81 and NRIs ranging from 0·34 to 0·57 in different region and sex combinations. When both BMI and WHtR were used, performance improved only slightly compared with using either adiposity measure alone. Interpretation BMI can distinguish young and middle-aged adults with higher versus lower amounts of abdominal adiposity with moderate-to-high accuracy, and both BMI and WHtR distinguish people with or without hypertension. However, at the same BMI level, people in south Asia, Latin America and the Caribbean, and the region of central Asia, Middle East and north Africa, have higher WHtR than in the other regions. Funding UK Medical Research Council and UK Research and Innovation (Innovate UK)