In this paper, we propose a new non-parametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines, and derive its theoretical properties including the asymptotically optimal...

We present a new method to sample random variables through the use of orthogonal polynomial expansions of the associated quantile function that utilize the inverse transform technique. In particular, we obtain an explicit representation of the quantile function through an orthogonal expansion...

We study a general and efficient nonparametric density estimation procedure for local bases, including B-splines, using a novel statistical Galerkin method, combined with basis duality theory. We provide an efficient cross-validation procedure to select the bandwidth, based on closed-form...

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 experienced recent advances in both theory and methodology. These estimators occupy a very interesting space in statistics,...

In this paper, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the moments of Student's t-distribution can be written in...

In this paper we study a conditional version of the Wang transform in the context of discrete GARCH models and their diffusion limits. Our first contribution shows that the conditional Wang transform and Duan's generalized local risk-neutral valuation relationship based on equilibrium...

This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk-neutralization is based on a variance dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a...

We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the...