A severe limitation of the original autoregressive process of order one or AR(1) process is the Gaussian nature of the assumed residual error distribution while the observed sample residual errors tend to be much more skewed and have a much higher kurtosis than is allowed by a normal...

The exact probability distribution of the first digit of integer powers up to an arbitrary but fixed number of digits is derived. Based on its asymptotic distribution, it is shown that it approaches Benford's law very closely for sufficiently high powers

Given integer-valued and more general real-valued wagers, Feller(1968), Ethier and Khoshnevisan(2002) have established upper and lower bounds on the probability of ruin, which often turn out to be very close to each other. However, the exact calculation of these bounds depends on the unique...

Building on a new theory of parametric risk models initiated in Hürlimann(1998), it is shown how mean scaled individual risk models can be constructed. The approximate computation of their distributions and related quantities can be done in the author's (1990) mathematical framework of...

Based on a non-parametric criterion of independence derived from a generalized version of the Schweizer-Wolff non-parametric measure of dependence, we calculate rates of convergence to asymptotic independence between the order statistics in a general setting. Three different rates of convergence...

The analytical evaluation of economic risk capital as well as the measurement and allocation of diversification for portfolios of non-normal risks is an open field in risk management research. Based on the method of copulas, we construct a parametric family of multivariate distributions using...

A copula based statistical method for fitting joint cumulative returns between a market index and a single stock to daily data is proposed. Modifying the method of inference functions for margins (IFM method), one performs two separate maximum likelihood estimations of the univariate marginal...

The class of bivariate extreme value copulas, which satisfies the monotone regression positive dependence property or equivalently the stochastic increasing property, is considered. A variational calculus proof of the Hutchinson-Lai conjecture about Kendall's tau and Spearman's rho for this...