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 body-mass index, underweight, overweight, and obesity from 1975 to 2016: a pooled analysis of 2416 population-based measurement studies in 128·9 million children, adolescents, and adults.

BACKGROUND: Underweight, overweight, and obesity in childhood and adolescence are associated with adverse health consequences throughout the life-course. Our aim was to estimate worldwide trends in mean body-mass index (BMI) and a comprehensive set of BMI categories that cover underweight to obesity in children and adolescents, and to compare trends with those of adults. METHODS: We pooled 2416 population-based studies with measurements of height and weight on 128·9 million participants aged 5 years and older, including 31·5 million aged 5-19 years. We used a Bayesian hierarchical model to estimate trends from 1975 to 2016 in 200 countries for mean BMI and for prevalence of BMI in the following categories for children and adolescents aged 5-19 years: more than 2 SD below the median of the WHO growth reference for children and adolescents (referred to as moderate and severe underweight hereafter), 2 SD to more than 1 SD below the median (mild underweight), 1 SD below the median to 1 SD above the median (healthy weight), more than 1 SD to 2 SD above the median (overweight but not obese), and more than 2 SD above the median (obesity). FINDINGS: Regional change in age-standardised mean BMI in girls from 1975 to 2016 ranged from virtually no change (-0·01 kg/m2 per decade; 95% credible interval -0·42 to 0·39, posterior probability [PP] of the observed decrease being a true decrease=0·5098) in eastern Europe to an increase of 1·00 kg/m2 per decade (0·69-1·35, PP>0·9999) in central Latin America and an increase of 0·95 kg/m2 per decade (0·64-1·25, PP>0·9999) in Polynesia and Micronesia. The range for boys was from a non-significant increase of 0·09 kg/m2 per decade (-0·33 to 0·49, PP=0·6926) in eastern Europe to an increase of 0·77 kg/m2 per decade (0·50-1·06, PP>0·9999) in Polynesia and Micronesia. Trends in mean BMI have recently flattened in northwestern Europe and the high-income English-speaking and Asia-Pacific regions for both sexes, southwestern Europe for boys, and central and Andean Latin America for girls. By contrast, the rise in BMI has accelerated in east and south Asia for both sexes, and southeast Asia for boys. Global age-standardised prevalence of obesity increased from 0·7% (0·4-1·2) in 1975 to 5·6% (4·8-6·5) in 2016 in girls, and from 0·9% (0·5-1·3) in 1975 to 7·8% (6·7-9·1) in 2016 in boys; the prevalence of moderate and severe underweight decreased from 9·2% (6·0-12·9) in 1975 to 8·4% (6·8-10·1) in 2016 in girls and from 14·8% (10·4-19·5) in 1975 to 12·4% (10·3-14·5) in 2016 in boys. Prevalence of moderate and severe underweight was highest in India, at 22·7% (16·7-29·6) among girls and 30·7% (23·5-38·0) among boys. Prevalence of obesity was more than 30% in girls in Nauru, the Cook Islands, and Palau; and boys in the Cook Islands, Nauru, Palau, Niue, and American Samoa in 2016. Prevalence of obesity was about 20% or more in several countries in Polynesia and Micronesia, the Middle East and north Africa, the Caribbean, and the USA. In 2016, 75 (44-117) million girls and 117 (70-178) million boys worldwide were moderately or severely underweight. In the same year, 50 (24-89) million girls and 74 (39-125) million boys worldwide were obese. INTERPRETATION: The rising trends in children's and adolescents' BMI have plateaued in many high-income countries, albeit at high levels, but have accelerated in parts of Asia, with trends no longer correlated with those of adults. FUNDING: Wellcome Trust, AstraZeneca Young Health Programme

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