Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

Advanced educational parallel DSP system based on TMS320C25 processors

This paper describes the design, application, and evaluation of a user friendly, flexible, scalable and inexpensive Advanced Educational Parallel (AdEPar) digital signal processing (DSP) system based on TMS320C25 digital processors to implement DSP algorithms. This system will be used in the DSP laboratory by graduate students to work on advanced topics such as developing parallel DSP algorithms. The graduating senior students who have gained some experience in DSP can also use the system. The DSP laboratory has proved to be a useful tool in the hands of the instructor to teach the mathematically oriented topics of DSP that are often difficult for students to grasp. The DSP laboratory with assigned projects has greatly improved the ability of the students to understand such complex topics as the fast Fourier transform algorithm, linear and circular convolution, the theory and design of infinite impulse response (IIR) and finite impulse response (FIR) filters. The user friendly PC software support of the AdEPar system makes it easy to develop DSP programs for students. This paper gives the architecture of the AdEPar DSP system. The communication between processors and the PC-DSP processor communication are explained. The parallel debugger kernels and the restrictions of the system are described. The programming in the AdEPar is explained, and two benchmarks (parallel FFT and DES) are presented to show the system performance.

Implementing and testing branch-and-bound algorithm for the quadratic 0-1 problem on transputers

Discrete optimization problems are very difficult to solve, even if the dimention is small. For most of them the problem of finding an ε-approximate solution is already NP-hard. The branch-and-bound algorithms are the most used algorithms for solving exactly this sort of problems.

Parallel rule induction with information theoretic pre-pruning

In a world where data is captured on a large scale the major challenge for data mining algorithms is to be able to scale up to large datasets. There are two main approaches to inducing classification rules, one is the divide and conquer approach, also known as the top down induction of decision trees; the other approach is called the separate and conquer approach. A considerable amount of work has been done on scaling up the divide and conquer approach. However, very little work has been conducted on scaling up the separate and conquer approach.In this work we describe a parallel framework that allows the parallelisation of a certain family of separate and conquer algorithms, the Prism family. Parallelisation helps the Prism family of algorithms to harvest additional computer resources in a network of computers in order to make the induction of classification rules scale better on large datasets. Our framework also incorporates a pre-pruning facility for parallel Prism algorithms.

Vectorized algorithms for quadtree construction and descent

This paper presents vectorized methods of construction and descent of quadtrees that can be easily adapted to message passing parallel computing. A time complexity analysis for the present approach is also discussed. The proposed method of tree construction requires a hash table to index nodes of a linear quadtree in the breadth-first order. The hash is performed in two steps: an internal hash to index child nodes and an external hash to index nodes in the same level (depth). The quadtree descent is performed by considering each level as a vector segment of a linear quadtree, so that nodes of the same level can be processed concurrently. © 2012 Springer-Verlag.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Many-core Algorithms for Combinatorial Optimization

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Parallel geostatistics for sparse and dense datasets

Very large spatially-referenced datasets, for example, those derived from satellite-based sensors which sample across the globe or large monitoring networks of individual sensors, are becoming increasingly common and more widely available for use in environmental decision making. In large or dense sensor networks, huge quantities of data can be collected over small time periods. In many applications the generation of maps, or predictions at specific locations, from the data in (near) real-time is crucial. Geostatistical operations such as interpolation are vital in this map-generation process and in emergency situations, the resulting predictions need to be available almost instantly, so that decision makers can make informed decisions and define risk and evacuation zones. It is also helpful when analysing data in less time critical applications, for example when interacting directly with the data for exploratory analysis, that the algorithms are responsive within a reasonable time frame. Performing geostatistical analysis on such large spatial datasets can present a number of problems, particularly in the case where maximum likelihood. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively. Most modern commodity hardware has at least 2 processor cores if not more. Other mechanisms for allowing parallel computation such as Grid based systems are also becoming increasingly commonly available. However, currently there seems to be little interest in exploiting this extra processing power within the context of geostatistics. In this paper we review the existing parallel approaches for geostatistics. By recognising that diffeerent natural parallelisms exist and can be exploited depending on whether the dataset is sparsely or densely sampled with respect to the range of variation, we introduce two contrasting novel implementations of parallel algorithms based on approximating the data likelihood extending the methods of Vecchia [1988] and Tresp [2000]. Using parallel maximum likelihood variogram estimation and parallel prediction algorithms we show that computational time can be significantly reduced. We demonstrate this with both sparsely sampled data and densely sampled data on a variety of architectures ranging from the common dual core processor, found in many modern desktop computers, to large multi-node super computers. To highlight the strengths and weaknesses of the diffeerent methods we employ synthetic data sets and go on to show how the methods allow maximum likelihood based inference on the exhaustive Walker Lake data set.

A Framework for Fast Classification Algorithms

Today, due to globalization of the world the size of data set is increasing, it is necessary to discover the knowledge. The discovery of knowledge can be typically in the form of association rules, classification rules, clustering, discovery of frequent episodes and deviation detection. Fast and accurate classifiers for large databases are an important task in data mining. There is growing evidence that integrating classification and association rules mining, classification approaches based on heuristic, greedy search like decision tree induction. Emerging associative classification algorithms have shown good promises on producing accurate classifiers. In this paper we focus on performance of associative classification and present a parallel model for classifier building. For classifier building some parallel-distributed algorithms have been proposed for decision tree induction but so far no such work has been reported for associative classification.

Numerical Results for the Generalized Mittag-Leffler Function

Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf

Parallel Problem Solving from Nature – PPSN XIV:14th International Conference, Edinburgh, UK, September 17-21, 2016, Proceedings

This book constitutes the refereed proceedings of the 14th International Conference on Parallel Problem Solving from Nature, PPSN 2016, held in Edinburgh, UK, in September 2016. The total of 93 revised full papers were carefully reviewed and selected from 224 submissions. The meeting began with four workshops which offered an ideal opportunity to explore specific topics in intelligent transportation Workshop, landscape-aware heuristic search, natural computing in scheduling and timetabling, and advances in multi-modal optimization. PPSN XIV also included sixteen free tutorials to give us all the opportunity to learn about new aspects: gray box optimization in theory; theory of evolutionary computation; graph-based and cartesian genetic programming; theory of parallel evolutionary algorithms; promoting diversity in evolutionary optimization: why and how; evolutionary multi-objective optimization; intelligent systems for smart cities; advances on multi-modal optimization; evolutionary computation in cryptography; evolutionary robotics - a practical guide to experiment with real hardware; evolutionary algorithms and hyper-heuristics; a bridge between optimization over manifolds and evolutionary computation; implementing evolutionary algorithms in the cloud; the attainment function approach to performance evaluation in EMO; runtime analysis of evolutionary algorithms: basic introduction; meta-model assisted (evolutionary) optimization. The papers are organized in topical sections on adaption, self-adaption and parameter tuning; differential evolution and swarm intelligence; dynamic, uncertain and constrained environments; genetic programming; multi-objective, many-objective and multi-level optimization; parallel algorithms and hardware issues; real-word applications and modeling; theory; diversity and landscape analysis.

ICTM: an interval tessellation-based model for reliable topographic segmentation

This work introduces a tessellation-based model for the declivity analysis of geographic regions. The analysis of the relief declivity, which is embedded in the rules of the model, categorizes each tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) sign of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into subregions of cells belonging to a same category, that is, presenting the same declivity sign. In order to control the errors coming from the discretization of the region into tessellation cells, or resulting from numerical computations, interval techniques are used. The implementation of the model is naturally parallel since the analysis is performed on the basis of local rules. An immediate application is in geophysics, where an adequate subdivision of geographic areas into segments presenting similar topographic characteristics is often convenient.

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.