Characterization of Probability Distributions by Variance Bounds and its Applications

Department of Statistics, Cochin University of Science and Technology

Fator estocástico de desconto: as cotas de variância, métricas de distância e suas extensões

The concept of stochastic discount factor pervades the Modern Theory of Asset Pricing. Initially, such object allows unattached pricing models to be discussed under the same terms. However, Hansen and Jagannathan have shown there is worthy information to be brought forth from such powerful concept which undelies asset pricing models. From security market data sets, one is able to explore the behavior of such random variable, determining a useful variance bound. Furthermore, through that instrument, they explore one pitfall on modern asset pricing: model misspecification. Those major contributions, alongside with some of its extensions, are thoroughly investigated in this exposition.

Oxygen variance and meridional oxygen supply in the Tropical North East Atlantic oxygen minimum zone

The distribution of the mean oceanic oxygen concentration results from a balance between ventilation and consumption. In the eastern tropical Pacific and Atlantic, this balance creates extended oxygen minimum zones (OMZ) at intermediate depth. Here, we analyze hydrographic and velocity data from shipboard and moored observations, which were taken along the 23°W meridian cutting through the Tropical North East Atlantic (TNEA) OMZ, to study the distribution and generation of oxygen variability. By applying the extended Osborn-Cox model, the respective role of mesoscale stirring and diapycnal mixing in producing enhanced oxygen variability, found at the southern and upper boundary of the OMZ, is quantified. From the well-ventilated equatorial region toward the OMZ core a northward eddy-driven oxygen flux is observed whose divergence corresponds to an oxygen supply of about 2.4 µmol kg-1 year-1 at the OMZ core depth. Above the OMZ core, mesoscale eddies act to redistribute low- and high-oxygen waters associated with westward and eastward currents, respectively. Here, absolute values of the local oxygen supply >10 mmol kg-1 year-1 are found, likely balanced by mean zonal advection. Combining our results with recent studies, a refined oxygen budget for the TNEA OMZ is derived. Eddy-driven meridional oxygen supply contributes more than 50 % of the supply required to balance the estimated oxygen consumption. The oxygen tendency in the OMZ, as given by the multidecadal oxygen decline, is maximum slightly above the OMZ core and represents a substantial imbalance of the oxygen budget reaching about 20 % of the magnitude of the eddy-driven oxygen supply.

Acclimatization to high-variance habitats does not enhance physiological tolerance of two key Caribbean corals to future temperature and pH

Corals are acclimatized to populate dynamic habitats that neighbour coral reefs. Habitats such as seagrass beds exhibit broad diel changes in temperature and pH that routinely expose corals to conditions predicted for reefs over the next 50-100 years. However, whether such acclimatization effectively enhances physiological tolerance to, and hence provides refuge against, future climate scenarios remains unknown. Also, whether corals living in low-variance habitats can tolerate present-day high-variance conditions remains untested. We experimentally examined how pH and temperature predicted for the year 2100 affects the growth and physiology of two dominant Caribbean corals (Acropora palmata and Porites astreoides) native to habitats with intrinsically low (outer-reef terrace, LV) and/or high (neighbouring seagrass, HV) environmental variance. Under present-day temperature and pH, growth and metabolic rates (calcification, respiration and photosynthesis) were unchanged for HV versus LV populations. Superimposing future climate scenarios onto the HV and LV conditions did not result in any enhanced tolerance to colonies native to HV. Calcification rates were always lower for elevated temperature and/or reduced pH. Together, these results suggest that seagrass habitats may not serve as refugia against climate change if the magnitude of future temperature and pH changes is equivalent to neighbouring reef habitats.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

Career development and personal functioning differences between work-bound and non-work bound students

We surveyed 506 Australian high school students on career development (exploration, planning, job-knowledge, decision-making, indecision), personal functioning (well-being, self-esteem, life satisfaction, school satisfaction) and control variables (parents’ education, school achievement), and tested differences among work-bound, college-bound and university-bound students. The work-bound students had the poorest career development and personal functioning, the university-bound students the highest, with the college-bound students falling in-between the other two groups. Work-bound students did poorest, even after controlling for parental education and school achievement. The results suggest a relationship between career development and personal functioning in high school students.

The distribution of the sample minimum-variance frontier

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios. Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution