The Experts below are selected from a list of 12417 Experts worldwide ranked by ideXlab platform
Chaohua Dong - One of the best experts on this subject based on the ideXlab platform.
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solving replication problems in a complete market by Orthogonal series Expansion
The North American Journal of Economics and Finance, 2013Co-Authors: Chaohua Dong, Jiti GaoAbstract:Abstract We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black–Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The main advantage of our method is that we propose using an Orthogonal Expansion method to derive a closed-form expression for the self-financing strategy that is associated with some general underlying asset processes. As a consequence, a replication strategy is obtained for a European option. Converse to the traditional Black–Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black–Scholes pricing formula. We provide an implementation procedure and both numerical and empirical examples to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black–Scholes theory.
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Orthogonal Expansion of levy process functionals theory and practice
Research Papers in Economics, 2013Co-Authors: Chaohua Dong, Jiti GaoAbstract:In this paper, Expansions of functionals of Levy processes are established under some Hilbert spaces and their Orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Levy processes are considered. Several Expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Levy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Simulations and empirical study are provided to illustrate the theoretical results.
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solving replication problems in complete market by Orthogonal series Expansion
Social Science Research Network, 2012Co-Authors: Jiti Gao, Chaohua DongAbstract:We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The departure of our method from the literature is, using an Orthogonal Expansion of a process related to the proposed trading strategy, we can construct a complete orthonormal basis for the space of cumulative gains in the complete market so that every self-financing strategy can be expressed as a combination of the basis. Hence, a replication strategy is obtained for a European option. Converse to the traditional Black-Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black-Scholes pricing formula. We then provide an implementation procedure to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black-Scholes theory.
Jiti Gao - One of the best experts on this subject based on the ideXlab platform.
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solving replication problems in a complete market by Orthogonal series Expansion
The North American Journal of Economics and Finance, 2013Co-Authors: Chaohua Dong, Jiti GaoAbstract:Abstract We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black–Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The main advantage of our method is that we propose using an Orthogonal Expansion method to derive a closed-form expression for the self-financing strategy that is associated with some general underlying asset processes. As a consequence, a replication strategy is obtained for a European option. Converse to the traditional Black–Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black–Scholes pricing formula. We provide an implementation procedure and both numerical and empirical examples to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black–Scholes theory.
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Orthogonal Expansion of levy process functionals theory and practice
Research Papers in Economics, 2013Co-Authors: Chaohua Dong, Jiti GaoAbstract:In this paper, Expansions of functionals of Levy processes are established under some Hilbert spaces and their Orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Levy processes are considered. Several Expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Levy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Simulations and empirical study are provided to illustrate the theoretical results.
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solving replication problems in complete market by Orthogonal series Expansion
Social Science Research Network, 2012Co-Authors: Jiti Gao, Chaohua DongAbstract:We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The departure of our method from the literature is, using an Orthogonal Expansion of a process related to the proposed trading strategy, we can construct a complete orthonormal basis for the space of cumulative gains in the complete market so that every self-financing strategy can be expressed as a combination of the basis. Hence, a replication strategy is obtained for a European option. Converse to the traditional Black-Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black-Scholes pricing formula. We then provide an implementation procedure to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black-Scholes theory.
Bernhard Sick - One of the best experts on this subject based on the ideXlab platform.
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Online Segmentation of Time Series Based on Polynomial Least-Squares Approximations
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010Co-Authors: Erich Fuchs, Thiemo Gruber, Jiri Nitschke, Bernhard SickAbstract:The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of Orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the Orthogonal Expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.
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processing short term and long term information with a combination of polynomial approximation techniques and time delay neural networks
IEEE Transactions on Neural Networks, 2009Co-Authors: Erich Fuchs, Christian Gruber, Tobias Reitmaier, Bernhard SickAbstract:Neural networks are often used to process temporal information, i.e., any kind of information related to time series. In many cases, time series contain short-term and long-term trends or behavior. This paper presents a new approach to capture temporal information with various reference periods simultaneously. A least squares approximation of the time series with Orthogonal polynomials will be used to describe short-term trends contained in a signal (average, increase, curvature, etc.). Long-term behavior will be modeled with the tapped delay lines of a time-delay neural network (TDNN). This network takes the coefficients of the Orthogonal Expansion of the approximating polynomial as inputs such considering short-term and long-term information efficiently. The advantages of the method will be demonstrated by means of artificial data and two real-world application examples, the prediction of the user number in a computer network and online tool wear classification in turning.
Olav Breinbjerg - One of the best experts on this subject based on the ideXlab platform.
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higher order hierarchical legendre basis functions for electromagnetic modeling
IEEE Transactions on Antennas and Propagation, 2004Co-Authors: E Jorgensen, John L Volakis, Peter Meincke, Olav BreinbjergAbstract:This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from Orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features. Expressions are presented for wire, surface, and volume elements but emphasis is given to the surface elements. In this case, the new hierarchical basis leads to a near-Orthogonal Expansion of the unknown surface current and implicitly an Orthogonal Expansion of the surface charge. In addition, all higher order terms in the Expansion have two vanishing moments. In contrast to existing formulations, these properties allow the use of very high-order basis functions without introducing ill-conditioning of the resulting MoM matrix. Numerical results confirm that the condition number of the MoM matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions. As a consequence of the excellent condition numbers, we demonstrate that even very high-order MoM systems, e.g., tenth order, can be solved efficiently with an iterative solver in relatively few iterations.
Erich Fuchs - One of the best experts on this subject based on the ideXlab platform.
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Online Segmentation of Time Series Based on Polynomial Least-Squares Approximations
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010Co-Authors: Erich Fuchs, Thiemo Gruber, Jiri Nitschke, Bernhard SickAbstract:The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of Orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the Orthogonal Expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.
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processing short term and long term information with a combination of polynomial approximation techniques and time delay neural networks
IEEE Transactions on Neural Networks, 2009Co-Authors: Erich Fuchs, Christian Gruber, Tobias Reitmaier, Bernhard SickAbstract:Neural networks are often used to process temporal information, i.e., any kind of information related to time series. In many cases, time series contain short-term and long-term trends or behavior. This paper presents a new approach to capture temporal information with various reference periods simultaneously. A least squares approximation of the time series with Orthogonal polynomials will be used to describe short-term trends contained in a signal (average, increase, curvature, etc.). Long-term behavior will be modeled with the tapped delay lines of a time-delay neural network (TDNN). This network takes the coefficients of the Orthogonal Expansion of the approximating polynomial as inputs such considering short-term and long-term information efficiently. The advantages of the method will be demonstrated by means of artificial data and two real-world application examples, the prediction of the user number in a computer network and online tool wear classification in turning.
