Asymptotics of work distributions: The pre-exponential factor

We determine the complete asymptotic behaviour of the work distribution in driven stochastic systems described by Langevin equations. Special emphasis is put on the calculation of the pre-exponential factor which makes the result free of adjustable parameters. The method is applied to various examples and excellent agreement with numerical simulations is demonstrated. For the special case of parabolic potentials with time-dependent frequencies, we derive a universal functional form for the asymptotic work distribution.Comment: 12 pages, 12 figure

Subtraction method in the second random--phase approximation: first applications with a Skyrme energy functional

We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.Comment: 1 tex, 16 figure

Exchange rates and fundamentals

Standard economic models hold that exchange rates are influenced by fundamental variables such as relative money supplies, outputs, inflation rates and interest rates. Nonetheless, it has been well documented that such variables little help predict changes in floating exchange rates Š that is, exchange rates follow a random walk. We show that the data do exhibit a related link suggested by standard models - that the exchange rate helps predict fundamentals. We also show analytically that in a rational expectations present value model, an asset price manifests near random walk behavior if fundamentals are I(1) and the factor for discounting future fundamentals is near one. We suggest that this may apply to exchange rates.

Taylor Rules and the Deutschmark-Dollar Real Exchange Rate

We explore the link between an interest rate rule for monetary policy and the behavior of the real exchange rate. The interest rate rule, in conjunction with some standard assumptions, implies that the deviation of the real exchange rate from its steady state depends on the present value of a weighted sum of inflation and output gap differentials. The weights are functions of the parameters of the interest rate rule. An initial look at German data yields some support for the model.

Accounting for Exchange Rate Variability in Present-Value Models When the Discount Factor is Near One

Nominal exchange rates in low-inflation advanced countries are nearly random walks. Engel and West (2003a) offer an explanation for this in the context of models in which the exchange rate is determined as the discounted sum of current and expected future fundamentals. Engel and West show that if the fundamentals are I(1), then as the discount factor approaches one, the exchange rate becomes indistinguishable from a random walk. An alternative explanation for the random-walk behavior of exchange rates is that there are some unobserved variables that drive exchange rates that follow near random walks. This paper takes the approach that both explanations are possible. We are able to measure how much of exchange-rate variation could be accounted for by the Engel-West explanation, despite the fact that we do not observe the information set of financial markets. We find that the observable fundamentals (money, income, prices, interest rates) may account for about 40 percent of the variance of changes in exchange rates under the assumption of discount factors near unity.

A Real Options Analysis of Automatic Milking Systems

Automatic, or robotic, milking systems have the potential to significantly change the way milk is produced on U.S. dairy farms. However, there is a high degree of uncertainty associated with adoption of this new technology. A real options approach is used to analyze the decision to replace an operational milking system with an automatic milking system. The most important source of uncertainty is shown to be the length of the technology's useful life. Under our assumptions, the automatic system is always an optimal investment if it is certain that it will last longer than the operational system being replaced.Livestock Production/Industries,

How Fast Can You Escape a Compact Polytope?

The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for compact polytopes. We also establish a quantitative uniform upper bound on the time required for every trajectory to escape the given polytope. In addition, we establish iteration bounds for termination of discrete linear loops via reduction to the continuous case

Exchange Rates and Fundamentals

We show analytically that in a rational expectations present value model, an asset price manifests near random walk behavior if fundamentals are I(1) and the factor for discounting future fundamentals is near one. We argue that this result helps explain the well known puzzle that fundamental variables such as relative money supplies, outputs, inflation and interest rates provide little help in predicting changes in floating exchange rates. As well, we show that the data do exhibit a related link suggested by standard models - that the exchange rate helps predict these fundamentals. The implication is that exchange rates and fundamentals are linked in a way that is broadly consistent with asset pricing models of the exchange rate.