The ground state of a Gross–Pitaevskii energy with general potential in the Thomas–Fermi limit

We study the ground state which minimizes a Gross–Pitaevskii energy with general non-radial trapping potential, under the unit mass constraint, in the Thomas–Fermi limit where a small parameter tends to 0. This ground state plays an important role in the mathematical treatment of recent experiments on the phenomenon of Bose–Einstein condensation, and in the study of various types of solutions of nonhomogeneous defocusing nonlinear Schrodinger equations. Many of these applications require delicate estimates for the behavior of the ground state near the boundary of the condensate, as the singular parameter tends to zero, in the vicinity of which the ground state has irregular behavior in the form of a steep corner layer. In particular, the role of this layer is important in order to detect the presence of vortices in the small density region of the condensate, understand the superfluid flow around an obstacle, and also has a leading order contribution in the energy. In contrast to previous approaches, we utilize a perturbation argument to go beyond the classical Thomas–Fermi approximation and accurately approximate the layer by the Hastings–McLeod solution of the Painleve–II equation. This settles an open problem, answered very recently only for the special case of the model harmonic potential. In fact, we even improve upon previous results that relied heavily on the radial symmetry of the potential trap. Moreover, we show that the ground state has the maximal regularity available, namely it remains uniformly bounded in the 1/2-Holder norm, which is the exact Holder regularity of the singular limit profile, as the singular parameter tends to zero. Our study is highly motivated by an interesting open problem posed recently by Aftalion, Jerrard, and Royo-Letelier, and an open question of Gallo and Pelinovsky, concerning the removal of the radial symmetry assumption from the potential trap

Do Farmers Hedge Optimally or by Habit? A Bayesian Partial-Adjustment Model of Farmer Hedging

Hedging is one of the most important risk management decisions that farmers make and has a potentially large role in the level of profit eventually earned from farming. Using panel data from a survey of Georgia farmers that recorded their hedging decisions for four years on three crops we examine the role of habit, demographics, farm characteristics, and information sources on the hedging decisions made by 106 different farmers. We find that the role of habit varies widely. Information sources are shown to have significant and large effects on the chosen hedge ratios. The farmer's education level, attitude toward technology adoption, farm profitability, and the ratio of acres owned to acres farmed also play important roles in hedging decisions.Bayesian econometrics, hedging decisions, habit formation, information sources, Agricultural Finance,

Do Farmers Hedge Optimally or by Habit? A Bayesian Partial-Adjustment Model of Farmer Hedging

Hedging is one of the most important risk management decisions that farmers make and has a potentially large role in the level of profit eventually earned from farming. Using panel data from a survey of Georgia farmers that recorded their hedging decisions for 4 years on four crops, we examine the role of habit, demographics, farm characteristics, and information sources on the hedging decisions made by 57 different farmers. We find that the role of habit varies widely and that estimation of a single habit effect suffers from aggregation bias. Thus, modeling farmer-level heterogeneity in the examination of habit and hedging is crucial.Bayesian econometrics, habit formation, hedging decisions, information sources, Agribusiness, Agricultural Finance, Farm Management, Financial Economics, Labor and Human Capital, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, C11, Q12, Q14,

Components of Grain Futures Price Volatility

We analyze the determinants of daily futures price volatility in corn, soybeans, wheat, and oats markets from 1986 to 2007. Combining the information from simultaneously traded contracts, a generalized least squares method is implemented that allows us to clearly distinguish among time-to-delivery effects, seasonality, calendar trend, and volatility persistence. We find strong evidence of time-to-delivery (Samuelson) effects and systematic seasonal components with volatility increasing prior to harvest times— an indirect confirmation of the theory of storage.futures markets, Samuelson effect, seasonality, time to maturity, volatility, Crop Production/Industries, Risk and Uncertainty,

Volatility Persistence in Commodity Futures:Inventory and Time-to-Delivery Effects

Most financial asset returns exhibit volatility persistence. We investigate this phenomenon in the context of daily returns in commodity futures markets. We show that the time gap between the arrival of news to the markets and the delivery time of futures contracts is the fundamental variable in explaining volatility persistence in the lumber futures market. We also find an inverse relationship between inventory levels and lumber futures volatility.volatility persistence, theory of storage, volatility, futures markets, lumber, Agricultural Finance,