G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE

We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms. For the linear case of G corresponding the classical Wiener probability space with Wiener measure P, we have established a 1-1 correspondence between BSDE and such new type of quasilinear PDE in the corresponding P-Sobolev space. When G is nonlinear, we also provide such 1-1 correspondence between a fully nonlinear PDE in the corresponding G-Sobolev space and BSDE driven by G-Brownian. Consequently, the existence and uniqueness of such type of fully nonlinear path-dependence PDE in G-Sobolev space have been obtained via a recent results of BSDE driven by G-Brownian motion.Comment: 22 page

Representation Theorems for Quadratic F{\cal F}-Consistent Nonlinear Expectations

In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "${\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the optional sampling theorem. More importantly, we show that any quadratic ${\cal F}$-consistent nonlinear expectation with a certain domination property must be a quadratic $g$-expectation. The main contribution of this paper is the finding of the domination condition to replace the one used in all the previous works, which is no longer valid in the quadratic case. We also show that the representation generator must be deterministic, continuous, and actually must be of the simple form

Aging, the urban-rural gap and disability trends: 19 years of experience in China - 1987 to 2006

As the age of a population increases, so too does the rate of disability. In addition, disability is likely to be more common in rural compared with urban areas. The present study aimed to examine the influence of rapid population changes in terms of age and rural/urban residence on the prevalence of disability. Data from the 1987 and 2006 China Sampling Surveys on Disability were used to estimate the impacts of rapid ageing and the widening urban-rural gap on the prevalence of disability. Stratum specific rates of disability were estimated by 5-year age-group and type of residence. The decomposition of rates method was used to calculate the rate difference for each stratum between the two surveys. The crude disability rate increased from 4.89% in 1987 to 6.39% in 2006, a 1.5% increase over the 19 year period. However, after the compositional effects from the overall rates of changing age-structure in 1987 and 2006 were eliminated by standardization, the disability rate in 1987 was 6.13%, which is higher than that in 2006 (5.91%). While in 1987 the excess due to rural residence compared with urban was ,1.0%, this difference increased to .1.5% by 2006, suggesting a widening disparity by type of residence. When rates were decomposed, the bulk of the disability could be attributed to ageing, and very little to rural residence. However, a wider gap in prevalence between rural and urban areas could be observed in some age groups by 2006. The increasing number of elderly disabled persons in China and the widening discrepancy of disability prevalence between urban and rural areas may indicate that the most important priorities for disability prevention in China are to reinforce health promotion in older adults and improve health services in rural communities

Effects of Prenatal and Early Life Malnutrition: Evidence from the Greek Famine

This paper examines the long run education and labor market effects from early-life exposure to the Greek 1941-42 famine. Given the short duration of the famine, we can separately identify the famine effects for cohorts exposed in utero, during infancy and at one year of age. We find that adverse outcomes due to the famine are largest for infants. Further, in our regression analysis we exploit the fact that the famine was more severe in urban than in rural areas. Consistent with our prediction, we find that urban-born cohorts show larger negative impacts on educational outcomes than the rural-born cohorts

Growth Mixture Modeling for Sequential Growth Processes

We re-visit the issue of “compensatory growth hypothesis”. The main idea is that some infants who experience substandard growth due to nutrition deficiency may grow faster than other children at a later age, and eventually catch up. We test this hypothesis using the data from the Cebu longitudinal study that records two developmental phases for each individual: the first developmental phase includes 12 bi-monthly records from age zero to age two, and the second developmental phase includes three records measured around age 7, 10 and 14. To test the compensatory growth hypothesis is to identify a subgroup in the sample that grows slower than others from age 0-2, but catches up from age 7-14. Being able to simultaneously identify the optimal number of subgroups that has qualitatively different growth trajectories and the growth trajectory within each subgroup based on empirical data is the major strength of growth mixture modeling technique

Does Famine Have a Long-Term Effect on Cohort Mortality? Evidence from the 1959-1961 Great Leap Forward Famine in China

Using individual mortality records from three cohorts of newborns (1954-1958, 1959-1962, and 1963-1967) from a large national fertility survey data conducted in 1988 in China, I examine the effect of being conceived or born during the 1959-1961 Great Leap Forward Famine on postnatal mortality. The results show strong evidence of a short-term (period) effect of the famine, caused directly by starvation or severe malnutrition during the period of the famine. After controlling for period mortality fluctuation, however, the famine-born cohort does not show higher postnatal mortality than either the pre-famine or the post-famine cohort – as would have been expected from the “fetal origins” hypothesis. Aggregate-level cross-temporal comparisons using published cohort population counts from China’s 1982 Census, 1990 Census, 1995 micro Census, 2000 Census, and 2005 micro Census lead to the same conclusion. The relevance of these new findings for the “fetal origins” hypothesis and the selection effect hypothesis is discussed