Automated Parameters for Troubled-Cell Indicators Using Outlier Detection

In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...

A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is...

An Improved and Simplified Full-Newton Step O(n) Infeasible Interior-Point Method for Linear Optimization

We present an improved version of an infeasible interior-point method for linear optimization published in 2006. In the earlier version each iteration consisted of one so-called feasibility step and a few---at most three---centering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the...

On search games that include ambush

We present a stochastic game that models ambush/search in a finite region Q which has area but no other structure. The searcher can search a unit area of Q in unit time or adopt an "ambush" mode for a certain period. The searcher "captures" the hider when the searched region contains the hider's location or if the hider moves while the searcher...

Adaptive and Sequential Gridding Procedures for the Abstraction and Verification of Stochastic Processes

This work is concerned with the generation of finite abstractions of general state-space processes to be employed in the formal verification of probabilistic properties by means of automatic techniques such as probabilistic model checkers. The work employs an abstraction procedure based on the partitioning of the state-space, which generates a...

Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and American-style Asian options and for discretely and continuously monitored versions. In the present paper...

A Krylov stability-corrected coordinate-stretching metho to simulate wave propagation in unbounded domains

The Krylov subspace projection approach is a well-established tool for the reducedorder modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to the time-domain solution of exterior wave problems. We use frequency-independent perfectly matched layers to...

On the Retrieval of the Directional Scattering Matrix from Directional Noise

The crosscorrelation of ambient acoustic noise observed at two receivers yields the impulse response between these receivers, assuming that the noise field is diffuse. In practical situations the noise field exhibits directionality, which imprints the angle-dependent correlation function. For the situation of a directional scatterer in a...

On the use of rigid body modes in the deflated preconditioned conjugate gradient method

Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...

Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Solutions over Unstructured Triangular Meshes

The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with...

Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options

The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price...

On the Convergence Behavior of IDR(s) and Related Methods

An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...

Maximal Lp-Regularity for Stochastic Evolution Equations

Transverse Electric Scattering on Inhomogeneous Objects: Spectrum of Integral Operator and Preconditioning

The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify very dense...

Invariance Kernels of Single-Input Planar Nonlinear Systems

The problem of determining invariance kernels for planar single-input nonlinear systems is considered. If K is a closed set, its invariance kernel is the largest subset of K with the property of being positively invariant for arbitrary measurable input signals. It is shown that the boundary of the invariance kernel is a concatenation of...

Saddlepoint Approximations for Expectations and an Application to CDO Pricing

We derive two types of saddlepoint approximations for expectations in the form of E[(X - K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case. The approximations are further extended to...

A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston’s Model

We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C.W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826–848...