Gaussian factor models futures and forward prices

Email: hyndman{at}mathstat.concordia.ca Received on 31 July 2006. Accepted on 19 March 2007. We completely characterize the futures price and forward priceof a risky asset (commodity) paying a stochastic dividend yield(convenience yield). The asset (commodity) price is modelledas an exponential affine function of a Gaussian factors process,while the interest rate and dividend yield are affine functionsof the factors process. The characterization we provide is basedon the method of stochastic flows. We believe this method leadsto simpler and more clear-cut derivations of the futures priceand forward price formulae than alternative methods. Hedginga long-term forward contract with shorter term futures contractsand bonds is also examined.     

Predicting stock returns and assessing prediction performance

Email: r.d.baker{at}salford.ac.uk Received on 1 November 2006. Accepted on 15 March 2007. We use regression methods to predict the expected monthly returnon stocks and the covariance matrix of returns, the predictorvariables being a company's ‘fundamentals’, suchas dividend yield and the history of previous returns. Predictionsare evaluated out of sample for shares traded on the LondonStock Exchange from 1976 to 2005. We explore and evaluate manymodelling and inferential approaches, including the use of weightedregression, discounted regression, shrinkage of regression coefficientsand the transformation to normality of predictor variables.We also investigate alternative covariance matrix models, suchas a two-index model and a shrinkage model. Using suitable statisticsto enable the out-of-sample performance of competing methodologiesto be compared is crucial, and we develop some new statisticsand a graphical aid for this purpose. What is original in thispaper is an evaluation of many modelling and inferential proceduresfor which conflicting claims have been made in the literatureand the development of new measures of portfolio performance.     

Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

A calibration algorithm for simulation-based pricing models

Don L. McLeish Department of Statistics and Actuarial Science, University of Waterloo, Waterloo,Ontario N2L 3G1, Canada Corresponding author. Email: mreesor{at}uwo.ca Email: dlmcleis{at}math.uwaterloo.ca Received on 20 February 2007. Accepted on 15 March 2007. Derivative pricing models require calibration to market conditionsin order to determine quantities such as hedging positions andthe prices of other instruments. For stochastic models and/orcomplex derivatives whose prices are not of an analytic form,prices must be computed via simulation and the calibration ismore difficult. A method to facilitate the calibration of simulation-basedpricing models is proposed. The algorithm uses a statisticallydesigned experiment to select the points at which simulationsare performed. The method is quite general as it is independentof the stochastic model for the underlying and allows for differentobjective functions that can incorporate information such asopen interest and volume. Furthermore, market prices from European-and/or American-style derivatives covering a range of strikeprices and maturities can be handled by this technique. Examplesshow the procedure is successful at calibrating well-known assetpricing models to both simulated and market data.     

An LMI-based approach for robust stabilization of time delay systems containing saturating actuators

Email: elhaous_fati{at}yahoo.fr Corresponding author. Email: elh_tissir{at}yahoo.fr Received on September 8, 2005; Accepted on July 24, 2006 This paper deals with the problem of robust stabilization foruncertain systems with input saturation and time delay in thestate. The parameter uncertainties are time-varying and unknownbut are norm bounded. Sufficient conditions obtained via a linearmatrix inequality formulation are stated to guarantee the localstabilization. The method of synthesis consists in determiningsimultaneously a state feedback control law and an associateddomain of safe admissible states for which the stability ofthe closed-loop system is guaranteed when control saturationseffectively occur. Numerical examples are used to demonstratethe effectiveness of the proposed design technique.     

Direct approximation of observer error linearization for nonlinear forced systems

Email: klaus{at}roebenack.de In this paper, we discuss a generalization of the extended Luenbergerobserver. Our approach can be interpreted as an approximateerror linearization. The design procedure which is formulatedin terms of Lie derivatives and Lie brackets can easily be implementedusing computer algebra software.     

On the Stability Analysis of Nonlinear Systems

The stability of nonautonomous delay differential equationsis studied via a combination of the global linerization andnonlinear variation of parameter techniques. Permanent address: Department of Mathematics, University ofElectronics Science & Technology of China, Chengdu, China.     

Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems

e-mail address: stynes{at}bureau.ucc.ie We consider singularly perturbed high-order elliptic two-pointboundary value problems of convection-diffusion type. Undersuitable hypotheses, the coercivity of the associated bilinearform is proved and a representation result for the solutionsof such problems is given. A family of Galerkin finite-elementmethods based on piecewise polynomial test/trial functions ona Shishkin mesh is constructed and proved to be convergent,uniformly in the perturbation parameter, in energy and Wnorms. Numerical results are presentedfor a second-order problem and fourth-order problems.     

Shape-preserving interpolation in R3

Received on 7 September 1993. Revised on 20 February 1996. In this paper we develop and test a simple automatic algorithmfor constructing curvature- and torsion-continuous interpolantsin R³ which are shape-preserving in a sense that takes intoaccount the convexity, torsion, coplanarity and collinearityinformation contained in the polygonal line connecting the interpolationpoints. This algorithm exploits the asymptotic properties ofa family of C² polynomial splines of non-uniform degree, whichtend to the above-mentioned polygonal line, as the segment degreestend to infinity. The performance of the algorithm is testedfor a three-dimensional data set, containing coplanar and collineargroups of points as well. E-mail address: kaklis{at}deslab.ntua.gr Tel.: +30-1-7721419Telefax: +30-1-7721408 E-mail address: menelaos{at}sccm.stanford.edu     

Estimates of the region of attraction of continuous-time cascade systems

Xiao-Song Yang Department of Mathematics, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Huimin Li Departments of Mathematics and Control and Engineering, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Corresponding author. Email: yangxs{at}cqupt.edu.cn Received on May 1, 2006; Accepted on October 6, 2006 In this paper, we first present some new sufficient conditionsfor global asymptotic stability of continuous-time cascade systems.Then, we give some detailed results on the region of attractionof continuous-time cascade systems. Some examples are presentedto illustrate these results.     

The Solution of a Statistical Decision Problem with Moving Boundaries by the Image Method

Temporary address: Department of Theoretical Physics, University of Manchester. A point executes Brownian motion in one dimension, startingfrom a known initial position. Its velocity at any time is asuperposition of a constant "drift" speed and a random, diffusivecomponent, the motion taking place between two absorbing boundarieswhich move towards one another with constant speeds. The probabilitydistribution for the particle position at any time is foundby the method of images. The problem occurred originally inthe detection of a small d.c. signal in a large amount of "white"noise, and this application is discussed.     

An analysis of the coupling of finite-element and Nystrm methods in acoustic scattering

In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results. E-mail: kirsch{at}am.uni-erlangen.de E-mail: monk{at}math.udel.edu     

Optimal boundary feedback stabilization of a string with moving boundary

Email: gugat{at}am.uni-erlangen.de Received on April 30, 2006; We consider a finite string that is fixed at one end and subjectto a feedback control at the other end which is allowed to move.We show that the behaviour is similar to the situation whereboth ends are fixed: As long as the movement is not too fast,the energy decays exponentially and for a certain parameterin the feedback law it vanishes in finite time. We considermovements of the boundary that are continuously differentiablewith a derivative whose absolute value is smaller than the wavespeed. We solve a problem of worst-case optimal feedback control,where the parameter in the feedback law is chosen such thatthe worst-case L^p-norm of the space derivative at the fixedend of the string is minimized (p [1, )). We consider the worstcase both with respect to the initial conditions and with respectto the boundary movement. It turns out that the parameter forwhich the energy vanishes in finite time is optimal in thissense for all p.     

Necessary conditions for infinite-horizon Volterra optimal control problems with time delay

Email: csfvega{at}dm.uba.ar Received on August 17, 2006; Accepted on September 8, 2007 Necessary conditions are proved for optimal control problemsinvolving an infinite horizon and terminal conditions at infinitywhose states are governed by Volterra integral equations withnon-linear time delay.     

Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

Email: valery{at}techunix.technion.ac.il Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established.     

Estimation and decomposition of cost efficiency in the health care food service sector: an extended stochastic frontier approach

K. M. Matawie School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith South DC NSW 1797, Australia Email: a.assaf{at}uws.edu.au Corresponding author. Email: k.matawie{at}uws.edu.au Received on 11 February 2007. Accepted on 14 September 2007. This paper introduces and implements an extended stochasticfrontier model to estimate and decompose cost efficiency (CE)in the health care foodservice sector. The interesting featureof this model is that it allows differentiation between thethree different types of efficiency: technical efficiency (TE),allocative efficiency (AE) and their associated CE. A completeillustration of these efficiencies is presented using a cross-sectionalsample of 101 hospital foodservice operations. Results showedthat the model and all its parameter coefficients were plausible,significant and satisfy all theoretical requirements. It wasalso clear that the average efficiency scores were lower forTE (80%) than AE (88%), indicating that TE is the main sourceof CE and requires further attention.     

Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

Email: vio{at}utgjiu.ro Received on September 12, 2007; Accepted on December 26, 2008 In this article, we discuss a quadratic control problem forlinear discrete-time systems with Markov perturbations in Hilbertspaces, which is linked to a discrete-time Riccati equationdefined on certain infinite-dimensional ordered Banach space.We prove that under stabilizability and stochastic uniform observabilityconditions, the Riccati equation has a unique, uniformly positive,bounded on N and stabilizing solution. Based on this result,we solve the proposed optimal control problem. An example illustratesthe theory.     

Estimation of nonlinear systems without a priori structural information and its application in Hammerstein model identification with dynamic nonlinearities

Email: er-wei-bai{at}uiowa.edu Received on July 30, 2005; Accepted on July 23, 2006 In the paper, we discuss identification of a nonlinear systemwithout structural information and propose two methods, thekernel method and the orthonormal basis method. The convergenceresults are established for both methods without a priori structuralinformation. We then apply the results to identification ofHammerstein models with an unknown dynamic nonlinearity. Itis also shown that identification of the linear part in Hammersteinmodels is possible with no knowledge of the dynamic nonlinearity.     

A semi-Markov maintenance model with credit rating application

Email: g.damico{at}unich.it Received on 6 December 2006. Accepted on 2 April 2008. The impact of a preventive rating maintenance policy on therating process is investigated through the definition of a semi-Markovmaintenance model with imperfect repair at random times. Theresults allow us to study the rating migrations process in thetransient and the asymptotic case.