Measurements, Models, Systems and Design

531 s.

Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

Expert systems and finite element structural analysis - a review

Finite element analysis of many engineering systems is practised more as an art than as a science . It involves high level expertise (analytical as well as heuristic) regarding problem modelling (e .g. problem specification,13; choosing the appropriate type of elements etc .), optical mesh design for achieving the specified accuracy (e .g . initial mesh selection, adaptive mesh refinement), selection of the appropriate type of analysis and solution13; routines and, finally, diagnosis of the finite element solutions . Very often such expertise is highly dispersed and is not available at a single place with a single expert. The design of an expert system, such that the necessary expertise is available to a novice to perform the same job even in the absence of trained experts, becomes an attractive proposition. 13; In this paper, the areas of finite element structural analysis which require experience and decision-making capabilities are explored . A simple expert system, with a feasible knowledge base for problem modelling, optimal mesh design, type of analysis and solution routines, and diagnosis, is outlined. Several efforts in these directions, reported in the open literature, are also reviewed in this paper

Transportation Management in a Distributed Logistic Consumption System Under Uncertainty Conditions

The problem of supply management in the supplier-to-consumer logistics transport system has been formed and solved. The novelty of the formulation of the problem consists in the integrated accounting of costs in the logistic system, which takes into account at the same time the cost of transporting products from suppliers to consumers, as well as the costs for each of the consumers to store the unsold product and losses due to possible shortages. The resulting optimization problem is no longer a standard linear programming problem. In addition, the work assumes that the solution of the problem should be sought taking into account the fact that the initial data of the problem are not deterministic. The analysis of traditional methods of describing the uncertainty of the source data. It is concluded that, given the rapidly changing conditions for the implementation of the delivery process in a distributed supplier-to-consumer system, it is advisable to move from a theoretical probability representation of the source data to their description in terms of fuzzy mathematics. At the same time, in particular, the fuzzy values of the demand for the delivered product for each consumer are determined by their membership functions.Distribution of supplies in the system is described by solving a mathematical programming problem with a nonlinear objective function and a set of linear constraints of the transport type. In forming the criterion, a technology is used to transform the membership functions of fuzzy parameters of the problem to its theoretical probabilistic counterparts – density distribution of demand values. The task is reduced to finding for each consumer the value of the ordered product, minimizing the average total cost of storing the unrealized product and losses from the deficit. The initial problem is reduced to solving a set of integral equations solved, in general, numerically. It is shown that in particular, important for practice, particular cases, this solution is achieved analytically.The paper states the insufficient adequacy of the traditionally used mathematical models for describing fuzzy parameters of the problem, in particular, the demand. Statistical processing of real data on demand shows that the parameters of the membership functions of the corresponding fuzzy numbers are themselves fuzzy numbers. Acceptable mathematical models of the corresponding fuzzy numbers are formulated in terms of bifuzzy mathematics. The relations describing the membership functions of the bifuzzy numbers are given. A formula is obtained for calculating the total losses to storage and from the deficit, taking into account the bifuzzy of demand. In this case, the initial task is reduced to finding the distribution of supplies, at which the maximum value of the total losses does not exceed the permissible value

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

The 1990 progress report and future plans

This document describes the progress and plans of the Artificial Intelligence Research Branch (RIA) at ARC in 1990. Activities span a range from basic scientific research to engineering development and to fielded NASA applications, particularly those applications that are enabled by basic research carried out at RIA. Work is conducted in-house and through collaborative partners in academia and industry. Our major focus is on a limited number of research themes with a dual commitment to technical excellence and proven applicability to NASA short, medium, and long-term problems. RIA acts as the Agency's lead organization for research aspects of artificial intelligence, working closely with a second research laboratory at JPL and AI applications groups at all NASA centers

Numerical Solution of Fuzzy Equations with Z-numbers using Neural Networks

In this paper, the uncertainty property is represented by the Z-number as the coefficients of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. We also extend the fuzzy equation into dual type, which is natural for linear-in-parameter nonlinear systems. The solutions of these fuzzy equations are the controllers when the desired references are regarded as the outputs. The existence conditions of the solutions (controllability) are proposed. Two types of neural networks are implemented to approximate solutions of the fuzzy equations with Z-number coefficients