First passage time for multivariate jump‐diffusion processes in finance and other areas of applications

The first passage time (FPT) problem is an important problem with a wide range of applications in science, engineering, economics, and industry. Mathematically, such a problem can be reduced to estimating the probability of a stochastic process first to reach a boundary level. In most important applications in the financial industry, the FPT problem does not have an analytical solution and the development of efficient numerical methods becomes the only practical avenue for its solution. Most of our examples in this contribution are centered around the evaluation of default correlations in credit risk analysis, where we are concerned with the joint defaults of several correlated firms, the task that is reducible to a FPT problem. This task represents a great challenge for jump‐diffusion processes (JDP). In this contribution, we develop further our previous fast Monte Carlo method in the case of multivariate (and correlated) JDP. This generalization allows us, among other things, to evaluate the default events of several correlated assets based on a set of empirical data. The developed technique is an efficient tool for a number of financial, economic, and business applications, such as credit analysis, barrier option pricing, macroeconomic dynamics, and the evaluation of risk, as well as for a number of other areas of applications in science and engineering, where the FPT problem arises. Copyright © 2008 John Wiley & Sons, Ltd.     

A genetic approach for strategic resource allocation planning

Enterprises often implement a measurement system to monitor their march towards their strategic goals. Although this way it is possible to assess the progress of each goal, there is no structured way to reconsider resource allocation to those goals and to plan an optimal (or near optimal) allocation scheme. In this study we propose a genetic approach to match each goal with an autonomous entity (agent) with a specific resource sharing behavior. The overall performance is evaluated through a set of functions and genetic algorithms are used to eventuate in approximate optimal behavior’s schemes. To outline the strategic goals of the enterprise we used the balanced scorecard method. Letting agents deploy their sharing behavior over simulation time, we measure the scorecard’s performance and detect distinguished behaviors, namely recommendations for resource allocation.     

Tighter approximation bounds for LPT scheduling in two special cases

$Q||C_{\max }$ denotes the problem of scheduling n jobs on m machines of different speeds such that the makespan is minimized. In the paper two special cases of $Q||C_{\max }$ are considered: case I, when $m?1$ machine speeds are equal, and there is only one faster machine; and case II, when machine speeds are all powers of 2 (2-divisible machines). Case I has been widely studied in the literature, while case II is significant in an approach to design so called monotone algorithms for the scheduling problem.We deal with the worst case approximation ratio of the classic list scheduling algorithm ‘Largest Processing Time (LPT)’. We provide an analysis of this ratio $\mathit{Lpt}/\mathit{Opt}$ for both special cases: For ‘one fast machine’, a tight bound of $(\sqrt{3}+1)/2\approx 1.3660$ is given. For 2-divisible machines, we show that in the worst case $1.3673<\mathit{Lpt}/\mathit{Opt}<1.4$. Besides, we prove another lower bound of $955/699>(\sqrt{3}+1)/2$ when LPT breaks ties arbitrarily.To our knowledge, the best previous lower and upper bounds were $(4/3,3/2?1/2m]$ in case I [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155–166], respectively $[4/3?1/3m,3/2]$ in case II [R.L. Graham, Bounds on multiprocessing timing anomalies, SIAM Journal on Applied Mathematics 17 (1969) 416–429; A. Kovács, Fast monotone 3-approximation algorithm for scheduling related machines, in: Proc. 13th Europ. Symp. on Algs. (ESA), in: LNCS, vol. 3669, Springer, 2005, pp. 616–627]. Moreover, Gonzalez et al. conjectured the lower bound 4/3 to be tight in the ‘one fast machine’ case [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155–166].     

Deformation Techniques for Sparse Systems

We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system. This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration. Research was partially supported by the following grants: UBACyT X112 (2004–2007), UBACyT X847 (2006–2009), PIP CONICET 2461, PIP CONICET 5852/05, ANPCyT PICT 2005 17-33018, UNGS 30/3005, MTM2004-01167 (2004–2007), MTM2007-62799 and CIC 2007–2008.     

The Analysis and the Representation of Balanced Complex Polytopes in 2D

In this paper, we deepen the theoretical study of the geometric structure of a balanced complex polytope (b.c.p.), which is the generalization of a real centrally symmetric polytope to the complex space. We also propose a constructive algorithm for the representation of its facets in terms of their associated linear functionals. The b.c.p.s are used, for example, as a tool for the computation of the joint spectral radius of families of matrices. For the representation of real polytopes, there exist well-known algorithms such as, for example, the Beneath–Beyond method. Our purpose is to modify and adapt this method to the complex case by exploiting the geometric features of the b.c.p. However, due to the significant increase in the difficulty of the problem when passing from the real to the complex case, in this paper, we confine ourselves to examine the two-dimensional case. We also propose an algorithm for the computation of the norm the unit ball of which is a b.c.p. This work was supported by INdAM-GNCS.     

A {(\frac 4 3) -} approximation algorithm for a special case of the two machine flow shop problem with several availability constraints

In this paper, we deal with a special case of the two-machine flow shop scheduling problem with several availability constraints on the second machine, under the resumable scenario. We develop an improved algorithm with a relative worst-case error bound of 4/3.     

Metabolic profiling using principal component analysis, discriminant partial least squares, and genetic algorithms

The aim of this study was to evaluate evolutionary variable selection methods in improving the classification of ¹H nuclear magnetic resonance (NMR) metabonomic profiles, and to identify the metabolites that are responsible for the classification. Human plasma, urine, and saliva from a group of 150 healthy male and female subjects were subjected to ¹H NMR-based metabonomic analysis. The ¹H NMR spectra were analyzed using two pattern recognition methods, principal component analysis (PCA) and partial least square discriminant analysis (PLS-DA), to identify metabolites responsible for gender differences. The use of genetic algorithms (GA) for variable selection methods was found to enhance the classification performance of the PLS-DA models. The loading plots obtained by PCA and PLS-DA were compared and various metabolites were identified that are responsible for the observed separations. These results demonstrated that our approach is capable of identifying the metabolites that are important for the discrimination of classes of individuals of similar physiological conditions.     

Ultra-slim laminated capillary array for high-speed DNA separation

We developed a new kind of capillary array for electrophoresis by using the numerical-control (NC) wiring technique conventionally used to produce printed-circuit boards. Laminating two polyimide sheets after laying cylindrical capillaries between them according to designed geometries, we fabricated a 16-lane laminated capillary array (LCA) 9.9 cm long, 7.2 cm wide, and 0.5 mm thick in which the effective length of all capillaries was only 10.9 cm. This compact LCA thus had separation columns as short as those in capillary array electrophoresis chips fabricated by lithography techniques. Like conventional capillary arrays, it also enabled pipetting-less direct injection of analytes from sample preparation plates. Using the LCA with LIF detection and a replaceable fluid sieving matrix, we demonstrated high-speed ssDNA fragment separations. At an electric field strength of 316 V/cm, 15 fragments ranging from 50 to 500 bases were completely separated within 5.8 min in all lanes. The lane-to-lane CV of migration time was only 0.38%, and the fragment size for which the resolution per base was 0.59 was 258 +/- 15 bases (average +/-SD).     

Bias sensitive spectral sensitivity in double -SiC:H pin structures

In this work we discuss the use of multilayer stacked structures (p(SiC:H)/i(SiC:H)/n(SiC:H)/p(SiC:H)/i(Si:H)/n(Si:H)) sandwiched between two transparent conductive contacts as colour sensing devices. The thickness and the absorption coefficient of both front and back p–i–n cells were specifically designed in order to achieve simultaneously high blue collection and red transmittance in the front cell and full green absorption and high red collection in the back cell. Electric and optical sensing methods were used for measuring the current–voltage characteristics and the spectral sensitivity, under different experimental conditions. Results show that the spectral sensitivity of the device is strongly modulated by the applied voltage, which allows colour selectivity. The results were supported by a physical model.