5,711 research outputs found
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 BlackâScholes 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
Fuzzy Supernova Templates I: Classification
Modern supernova (SN) surveys are now uncovering stellar explosions at rates
that far surpass what the world's spectroscopic resources can handle. In order
to make full use of these SN datasets, it is necessary to use analysis methods
that depend only on the survey photometry. This paper presents two methods for
utilizing a set of SN light curve templates to classify SN objects. In the
first case we present an updated version of the Bayesian Adaptive Template
Matching program (BATM). To address some shortcomings of that strictly Bayesian
approach, we introduce a method for Supernova Ontology with Fuzzy Templates
(SOFT), which utilizes Fuzzy Set Theory for the definition and combination of
SN light curve models. For well-sampled light curves with a modest signal to
noise ratio (S/N>10), the SOFT method can correctly separate thermonuclear
(Type Ia) SNe from core collapse SNe with 98% accuracy. In addition, the SOFT
method has the potential to classify supernovae into sub-types, providing
photometric identification of very rare or peculiar explosions. The accuracy
and precision of the SOFT method is verified using Monte Carlo simulations as
well as real SN light curves from the Sloan Digital Sky Survey and the
SuperNova Legacy Survey. In a subsequent paper the SOFT method is extended to
address the problem of parameter estimation, providing estimates of redshift,
distance, and host galaxy extinction without any spectroscopy.Comment: 26 pages, 12 figures. Accepted to Ap
Recommended from our members
A conceptual design tool: Sketch and fuzzy logic based system
A real time sketch and fuzzy logic based prototype system for conceptual design has been developed. This system comprises four phases. In the first one, the system accepts the input of on-line free-hand sketches, and segments them into meaningful parts by using fuzzy knowledge to detect corners and inflection points on the sketched curves. The fuzzy knowledge is applied to capture userâs drawing intention in terms of sketching position, direction, speed and acceleration. During the second phase, each segmented sub-part (curve) can be classified and identified as one of the following 2D primitives: straight lines, circles, circular arcs, ellipses, elliptical arcs or B-spline curves. Then, 2D topology information (connectivity, unitary constraints and pairwise constraints) is extracted dynamically from the identified 2D primitives. From the extracted information, a more accurate 2D geometry can be built up by a 2D geometric constraint solver. The 2D topology and geometry information is then employed to further interpretation of a 3D geometry. The system can not only accept sketched input, but also usersâ interactive input of 2D and 3D primitives.
This makes it friendly and easier to use, in comparison with âsketched input onlyâ, or âinteractive input onlyâ systems.
Finally, examples are given to illustrate the system
Exploiting zoning based on approximating splines in cursive script recognition
Because of its complexity, handwriting recognition has to exploit many sources of information to be successful, e.g. the handwriting zones. Variability of zone-lines, however, requires a more flexible representation than traditional horizontal or linear methods. The proposed method therefore employs approximating cubic splines. Using entire lines of text rather than individual words is shown to improve the zoning accuracy, especially for short words. The new method represents an improvement over existing methods in terms of range of applicability, zone-line precision and zoning-classification accuracy. Application to several problems of handwriting recognition is demonstrated and evaluated
Monotonicity preserving approximation of multivariate scattered data
This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.<br /
An evolutionary approach to constraint-regularized learning
The success of machine learning methods for inducing models from data
crucially depends on the proper incorporation of background knowledge about
the model to be learned. The idea of constraint-regularized learning is to em-
ploy fuzzy set-based modeling techniques in order to express such knowl-
edge in a flexible way, and to formalize it in terms of fuzzy constraints.
Thus, background knowledge can be used to appropriately bias the learn-
ing process within the regularization framework of inductive inference. After
a brief review of this idea, the paper offers an operationalization of constraint-
regularized learning. The corresponding framework is based on evolutionary
methods for model optimization and employs fuzzy rule bases of the Takagi-
Sugeno type as flexible function approximators
Monotone approximation of aggregation operators using least squares splines
The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.<br /
- âŚ