For order $q$ kernel density estimators we show that the constant $b_q$ in $bias=b_qh^q+o(h^q)$ can be made arbitrarily small, while keeping the variance bounded. A data-based selection of bq is presented and Monte Carlo simulations illustrate the advantages of the method.

Since the 2008 financial crisis, modeling of the extreme values of financial risk has become important. Postgraduate programs and PhD research programs in mathematical finance are cropping up in nearly every university. Additionally, many conferences are being held annually on the topic of...

Blockchain and cryptocurrencies have recently captured the interest of academics and those in industry. Cryptocurrencies are essentially digital currencies that use blockchain technology and cryptography to facilitate secure and anonymous transactions. The cryptocurrency market is currently...

With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms...

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate...

Most of the financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation-based methods. In this paper, we examine the Filtered Historical Simulation (FHS) model introduced by Barone-Adesi et al. (1999) theoretically and empirically. The main goal...

The Pareto classical distribution is one of the most attractive in statistics and particularly in the scenario of actuarial statistics and finance. For example, it is widely used when calculating reinsurance premiums. In the last years, many alternative distributions have been proposed to obtain...

Cryptocurrencies are essentially digital currencies that use blockchain technology and cryptography to facilitate secure and anonymous transactions. Many institutions and countries are starting to understand and implement the idea of cryptocurrencies in their business models. With this recent...

It is shown that the total amount of income earned during a reference period can be expressed as the products of components of bivariate Pareto distributions. The exact distribution of the total amount of income P = XY and the corresponding moment properties are derived when (X, Y ) follows...