Technical inefficiency and public capital in US States: A stochastic frontier approach

This paper estimates a translog stochastic frontier production function in the analysis of all 48 contiguous U.S. states in the period 1970-1983, to attempt to measure and explain changes in technical efficiency. The model allows technical inefficiency to vary over time, and inefficiency effects to be a function of a set of explanatory variables in which the level and composition of public capital plays an important role. Results indicated that U.S. state inefficiency levels were significantly and positively correlated with the ratio of public capital to private capital. The proportion of public capital devoted to highways is negatively correlated with technical inefficiency, suggesting that not only the level but also the composition of public capital influenced state efficiency.

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.

Notes on stochastic choice

A general formalism on stochastic choice is presented. Tje Rationalizability and Recoverability (Identification) problems are discussed. For the identification issue parametric examples are analyzed by means of techniques of mathematical tomography (Random transforms).

Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped.

Value and depreciation of mineral resources over the very long run: An empirical contrast of different methods

The paper contrasts empirically the results of alternative methods for estimating thevalue and the depreciation of mineral resources. The historical data of Mexico andVenezuela, covering the period 1920s-1980s, is used to contrast the results of severalmethods. These are the present value, the net price method, the user cost method andthe imputed income method. The paper establishes that the net price and the user costare not competing methods as such, but alternative adjustments to different scenariosof closed and open economies. The results prove that the biases of the methods, ascommonly described in the theoretical literature, only hold under the most restrictedscenario of constant rents over time. It is argued that the difference between what isexpected to happen and what actually did happen is for the most part due to a missingvariable, namely technological change. This is an important caveat to therecommendations made based on these models.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

Cost efficiency in primary care contracting: A stochastic frontier cost function approach

The principal aim of this paper is to estimate a stochastic frontier costfunction and an inefficiency effects model in the analysis of the primaryhealth care services purchased by the public authority and supplied by 180providers in 1996 in Catalonia. The evidence from our sample does not supportthe premise that contracting out has helped improve purchasing costefficiency in primary care. Inefficient purchasing cost was observed in thecomponent of this purchasing cost explicitly included in the contract betweenpurchaser and provider. There are no observable incentives for thecontracted-out primary health care teams to minimise prescription costs, whichare not explicitly included in the present contracting system.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Inventory-routing model, for a multi-period problem with stochastic and deterministic demand

The need for integration in the supply chain management leads us to considerthe coordination of two logistic planning functions: transportation andinventory. The coordination of these activities can be an extremely importantsource of competitive advantage in the supply chain management. The battle forcost reduction can pass through the equilibrium of transportation versusinventory managing costs. In this work, we study the specific case of aninventory-routing problem for a week planning period with different types ofdemand. A heuristic methodology, based on the Iterated Local Search, isproposed to solve the Multi-Period Inventory Routing Problem with stochasticand deterministic demand.