Energy transactions in liberalized markets are subject to price and quantity uncertainty. This paper considers the spot energy generation follow a bivariate semi-nonparametric distribution defined terms of Gram–Charlier expansion. allows us jointly model not only mean, variance, correlation but also skewness, kurtosis, higher-order moments. Based on this model, we propose static hedging strateg...

We consider several generalizations of rook polynomials. In particular we develop analogs of the theory of rook polynomials that are related to general Laguerre and Charlier polynomials in the same way that ordinary rook polynomials are related to simple Laguerre polynomials.

In the present paper, we study some approximation properties of the Szász type operators involving Charlier polynomials introduced by Varma and Taşdelen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

In this paper we estimate the skewness of unconditional distribution energy returns and test its statistical significance. We compare performance traditional robust tests for with those based on implied in a TGARCH model Gram-Charlier (TGARCH-GC) innovations. also analyze implications TGARCH-GC tail risk through evaluation Value-at-Risk (VaR) expected shortfall (ES) accuracy. Our results show t...

Degenerate Dowling and degenerate r-Dowling polynomials were introduced earlier as versions further generalizations of polynomials. The aim this paper is to show their connections with Poisson central moments for a random variable certain parameter Charlier

We show that the Meixner, Pollaczek, Meixner-Pollaczek and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures. We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials. Running Title: Generating Functions