Cost minimization and the stochastic discount factor

It is shown that a cost function subject to internal costs of adjustment induces a stochastic discount factor (pricing kernel) that is a function of random output, input and output prices, existing capital stock, and investment. The only assumption on firm preferences is that they are increasing in current period consumption and future stochastic consumption. This ensures that the firm will always act to minimize current period cost of providing future consumption, and it is the first-order conditions for this cost minimization problem that generate the stochastic discount factor, which itself can be interpreted as the marginal variable cost of varying stochastic output. A cost-based pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data for the S&P 500 and commercial paper.     

Context equivalence of semigroups

Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.     

The structure and expression of power group

With the application of the topological upgrade, more and more experts are interested in the problems concerning the mathematical structure’s upgrade to its power set. This paper is a further study on the structure and interrelationship of a power group. By revealing the nature of relationship between the power group and a regular one, the present paper proves some theorems of the structure of the power group and constructs some theorems on its homomorphism and isomorphism as well, proposing an expression form and isomorphism replacement construct methods of the power group.     

The Existence and Uniqueness of the Solution for Neutral Stochastic Functional Differential Equations with Infinite Delay in Abstract Space

The main aim of this paper is to prove the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay, which the initial data belong to the phase space ℬ((−∞,0];ℝ ^d ). The vital work of this paper is to extend the initial function space of the paper (Wei and Wang, J. Math. Anal. Appl. 331:516–531, 2007) and give some examples to show that the phase space ℬ((−∞,0];ℝ ^d ) exists. In addition, this paper builds a Banach space ℳ²((−∞,T],ℝ ^d ) with a new norm in order to discuss the existence and uniqueness of the solution for such equations with infinite delay.     

(<Emphasis Type="Italic">δ</Emphasis>,<Emphasis Type="Italic">δ</Emphasis>′)-continuity on generalized topological spaces

We introduce the notion of (δ,δ′)-continuous functions on generalized topological spaces and investigate characterizations for such functions. We study the relationship between (δ,δ′)-continuity and several types of continuity on generalized topological spaces.     

Imaging of periodic dielectrics

We consider imaging of periodic penetrable structures from measurements of scattered electromagnetic waves. The importance of this problem stems from the decreasing size of periodic structures in photonic devices, together with an increasing demand in fast non-destructive testing. This demand makes qualitative inverse scattering techniques particularly attractive since they do not use time consuming optimization techniques for reconstruction but rather directly transform measured data into a picture of the scattering object. We present the Factorization method as an algorithm for imaging of a special class of periodic dielectric structures known as diffraction gratings. Our sampling method computes a picture of the shape of the periodic structure from measured near-field data in a rapid way. We provide numerical examples illustrating this imaging technique.     

On the Asymptotic Behavior of Solutions of the Heat Equation with a Random,Long-Range Correlated Potential

In this note we investigate the asymptotic behavior of the solutions of the heat equation with random, fast oscillating potential

A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

This paper considers complexity bounds for the problem of approximating the global minimum of a univariate function when the function evaluations are corrupted by random noise. We take an average-case point of view, where the objective function is taken to be a sample function of a Wiener process and the noise is independent Gaussian. Previous papers have bounded the convergence rates of some nonadaptive algorithms. We establish a lower bound on the convergence rate of any nonadaptive algorithm.     

Sequences of bias-adjusted covariance matrix estimators under heteroskedasticity of unknown form

The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and a set of explanatory variables. The assumption that all error variances are the same, known as homoskedasticity, is oftentimes violated when cross sectional data are used. Consistent standard errors for the ordinary least squares estimators of the regression parameters can be computed following the approach proposed by White (Econometrica 48:817–838, 1980). Such standard errors, however, are considerably biased in samples of typical sizes. An improved covariance matrix estimator was proposed by Qian and Wang (J Stat Comput Simul 70:161–174, 2001). In this paper, we improve upon the Qian–Wang estimator by defining a sequence of bias-adjusted estimators with increasing accuracy. The numerical results show that the Qian–Wang estimator is typically much less biased than the estimator proposed by Halbert White and that our correction to the former can be quite effective in small samples. Finally, we show that the Qian–Wang estimator can be generalized into a broad class of heteroskedasticity-consistent covariance matrix estimators, and our results can be easily extended to such a class of estimators.     

Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.