Handbook of Computational Methods for Integration

Kythe, Prem K.; Schaferkotter, Michael

doi:10.1201/9780203490303

Cited by 143 publications

(146 citation statements)

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“…The Gauss-Laguerre quadrature rule, which is an efficient way to evaluate integrals on semiinfinite domains, is then applied to handle the above integral (Kythe and Schaferkotter, 2014). In Algorithm 1, we present an algorithm to compute V (S, τ ).…”

Section: Numerical Proceduresmentioning

confidence: 99%

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A decomposition approach via Fourier sine transform for valuing American knock-out options with rebates

Dang

Khanh

2017

Journal of Computational and Applied Mathematics

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We present an innovative decomposition approach for computing the price and the hedging parameters of American knock-out options with a time-dependent rebate. Our approach is built upon: (i) the Fourier sine transform applied to the partial differential equation with a finite time-dependent spatial domain that governs the option price, and (ii) the decomposition technique that partitions the price of the option into that of the European counterpart and an early exercise premium. Our analytic representations can generalize a number of existing decomposition formulas for some European-style and American-style options. A complexity analysis of the method, together with numerical results, show that the proposed approach is significantly more efficient than the state-of-the-art adaptive finite difference methods, especially in dealing with spot prices near the barrier. Numerical results are also examined in order to provide new insight into the significant effects of the rebate on the option price, the hedging parameters, and the optimal exercise boundary.

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Section: Numerical Proceduresmentioning

confidence: 99%

“…Most of the integrals in these quantities are of smooth functions on finite domains and can be approximated by using the composite Gauss-Legendre rule (Kythe and Schaferkotter, 2014). The only one term that needs special attention is the second term of…”

Section: Numerical Proceduresmentioning

confidence: 99%

A decomposition approach via Fourier sine transform for valuing American knock-out options with rebates

Dang

Khanh

2017

Journal of Computational and Applied Mathematics

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“…A Gaussian quadrature (or a Gaussian collocation set) [11] is usually used as the one-dimensional integral rule in classical spectral methods such as the PCM (DEMM).…”

Section: Probabilistic Collocation For Statistical Analysis Of Contromentioning

confidence: 99%

“…Gautschi [12] showed that the performance of discretization can be increased through multi-component discretization. After constructing an orthonormal set with respect to the arbitrary measure, the collocation point and its corresponding weight in the Gaussian quadrature are given by [11]:…”

Section: Polynomial Chaos For Arbitrary Distribution and Its Associatmentioning

confidence: 99%

Robust PID controller design for processes with stochastic parametric uncertainties

Duong

Lee

2012

Journal of Process Control

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a b s t r a c tThe stability and performance of a system can be inferred from the evolution of statistical characteristics of the system's states. Wiener's polynomial chaos can provide an efficient framework for the statistical analysis of dynamical systems, computationally far superior to Monte Carlo simulations. This work proposes a new method of robust PID controller design based on polynomial chaos for processes with stochastic parametric uncertainties. The proposed method can greatly reduce computation time and can also efficiently handle both nominal and robust performance against stochastic uncertainties by solving a simple optimization problem. Simulation comparison with other methods demonstrated the effectiveness of the proposed design method.

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“…The Gauss-Jacobi quadrature addresses this problem; [73,74] approximate an integral having a singular integrand using Gaussian integration, namely,…”

Section: Gauss-jacobi Quadraturementioning

confidence: 99%