We develop a method for pricing financial options under uncertain volatility. The method is based on the dynamic programming principle and a Fourier cosine expansion method. Local errors in the vicinity of domain boundaries, originating from the use of Fourier series expansions, may hamper the algorithm’s convergence. We use an extrapolation method to deal with these errors.

Recently S. Tikhonov proved two theorems on the integrability of sine and cosine series with coefficients from the R 0 BV S class. These results are extended such that the R 0 BV S class is replaced by the MRBV S class.

Each Discrete Cosine Transform uses N real basis vectors whose components are cosines. In the DCT-4, for example, the jth component of v k is cos(j + 1 2)(k + 1 2) N. These basis vectors are orthogonal and the transform is extremely useful in image processing. If the vector x gives the intensities along a row of pixels, its cosine series P c k v k has the coeecients c k = (x; v k)=N. They are q...

We propose a new time series model aimed at forecasting crude oil prices. The proposed specification is an unobserved components model with an asymmetric cyclical component. The asymmetric cycle is defined as a sine-cosine wave where the frequency of the cycle depends on past oil price observations. We show that oil price forecasts improve significantly when this asymmetry is explicitly modelled.

In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when surplus process is observed at high frequency. The constructed based on Fourier–Cosine series expansion and its consistency property thoroughly studied. Simulation examples reveal that our performs better than Fourier transform method sample size finite.

Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...

We present a technique to make a close enough recognition of a function, based on recognition coefficients. The recognition coefficients are determined using inner products 5 of the function to be recognized with a complete set of functions. This is how generalized Fourier coefficients are calculated. However they may not give a series representation of the function to be recognized as the comp...

Large classes of standard single-field slow-roll inflationary models consistent with the required number e-folds, current bounds on spectral index scalar perturbations, tensor-to-scalar ratio, and scale inflation can be efficiently constructed using genetic algorithms. The setup is modular easily adapted to include further phenomenological constraints. A semi-comprehensive search for sextic pol...

Abstract We prove two conjectural identities of Z.-W. Sun concerning Apéry-like series. One the series is alternating, whereas other one not. Our main strategy to convert and alternating log-sine-cosine log-sinh-cosh integrals, respectively. Then we express all these integrals using single-valued Bloch–Wigner–Ramakrishnan–Wojtkowiak–Zagier polylogarithms. The conjectures then follow from a few ...