This work reviews the literature on spline local basis methods for non-parametric density
estimation. Particular attention is paid to B-spline density estimators which have …

The Fourier cosine expansion (COS) method is used for pricing European options
numerically very fast. To apply the COS method, a truncation range for the density of the log …

Recently, the valuation of variable annuity products has become a hot topic in actuarial
science. In this paper, we use the Fourier cosine series expansion (COS) method to value …

In this paper, we propose a general data-driven framework that unifies the valuation and risk
measurement of financial derivatives, which is especially useful in markets with thinly-traded …

In this article, we propose a new nonparametric density estimator derived from the theory of
frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density …

A general and efficient nonparametric density estimation procedure for local bases,
including B-splines, is proposed, which employs a novel statistical Galerkin method …

In this paper, we study the statistical estimation of the discounted density of the deficit at ruin
in the classical risk model. The estimator is constructed by the two-dimensional Fourier …

Learning density estimation is important in probabilistic modeling and reasoning with
uncertainty. Since B-spline basis functions are piecewise polynomials with local support …

In this work, we propose an efficient and robust valuation of discretely monitored arithmetic
Asian options based on Shannon wavelets. We employ the so-called SWIFT method, a …

This paper proposes the option-implied Fourier-cosine method, iCOS, for non-parametric
estimation of risk-neutral densities, option prices, and option sensitivities. The iCOS method …