UNDERSTANDING WORLD COMMODITY PRICES Returns, Volatility and Diversification

In recent times, the prices of internationally-traded commodities have reached record highs and there is considerable uncertainty regarding their future. This phenomenon is partially driven by strong demand from a small number of emerging economies, such as China and India. This paper places the recent commodity price boom in historical context, drawing on an investigation of the long-term time-series properties, and presents unique features for 33 individual commodity prices. Using a new methodology for examining cross-sectional variation of commodity returns and its components, we find strong evidence that the prices of world primary commodities are extremely volatile. In addition, prices are roughly 30 percent more volatile under floating than under fixed exchange rate regimes. Finally, using the capital asset pricing model as a loose framework, we find that global macroeconomic risk components have become relatively more important in explaining commodity price volatility.

Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Construction and Refinement of Coarse-Grained Models

A general scheme, which includes constructions of coarse-grained (CG) models, weighted ensemble dynamics (WED) simulations and cluster analyses (CA) of stable states, is presented to detect dynamical and thermodynamical properties in complex systems. In the scheme, CG models are efficiently and accurately optimized based on a directed distance from original to CG systems, which is estimated from ensemble means of lots of independent observable in two systems. Furthermore, WED independently generates multiple short molecular dynamics trajectories in original systems. The initial conformations of the trajectories are constructed from equilibrium conformations in CG models, and the weights of the trajectories can be estimated from the trajectories themselves in generating complete equilibrium samples in the original systems. CA calculates the directed distances among the trajectories and groups their initial conformations into some clusters, which correspond to stable states in the original systems, so that transition dynamics can be detected without requiring a priori knowledge of the states.Comment: 4 pages, no figure

Properties of Catlin's reduced graphs and supereulerian graphs

A graph $G$ is called collapsible if for every even subset $R\subseteq V(G)$, there is a spanning connected subgraph $H$ of $G$ such that $R$ is the set of vertices of odd degree in $H$. A graph is the reduction of $G$ if it is obtained from $G$ by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs $G$ of order $n$ with $d(u)+d(v)\ge 2(n/p-1)$ for any $uv\in E(G)$ where $p>0$ are given, we show how such graphs change if they have no spanning Eulerian subgraphs when $p$ is increased from $p=1$ to 10 then to $15$