This article provides efficient methods based on the saddlepoint approximation for computing the value at risk and the tail value at risk of the doubly compound and perturbed insurer total claim amount. The model is based on a primary counting birth process, for the number of catastrophic events, and on a secondary counting distribution, with possible modification or truncation at zero, for the...

For { t y } a discrete time, second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients , jk α j=1, … , k, of the best linear predictor of 1 + k y , , ˆ 1 1 1 y y y kk k k k α α − − − = + L best in the sense of minimizing the mean square error. The coefficients jk α determine a Levinson-Durbin sequence. A generalized Levinson-Durbin sequence, a special ...

Safety analysts usually use post-modeling methods, such as the Goodness-of-Fit statistics or the Likelihood Ratio Test, to decide between two or more competitive distributions or models. Such metrics require all competitive distributions to be fitted to the data before any comparisons can be accomplished. Given the continuous growth in introducing new statistical distributions, choosing the bes...

Traditional techniques for calculating control limits for processes with discrete responses are based on the Poisson distribution. However, for many processes, the assumption of a Poisson distribution is violated. In such cases, use of traditional Poisson control limits may result in an inflated risk of Type I error. The negative binomial distribution is a natural extension of the Poisson distr...

The need for investment in the improvement and expansion of the electric transmission grid has not been met in the new competitive environment. Investment in transmission assets poses demanding challenges: multiplicity of players, market imperfections, among others. The integration of financial instruments poses also an additional level of complication, because investors wish to ensure steady l...

We derive a quantile-adjusted conditional maximum likelihood estimator for the dispersion parameter of the negative binomial distribution and compare its performance, in terms of bias, to various other methods. Our estimation scheme outperforms all other methods in very small samples, typical of those from serial analysis of gene expression studies, the motivating data for this study. The impac...

The question of optimal strategic asset allocation for investors with behavioural utilities saving for retirement is addressed. To date this problem has been studied assuming that an investor is rational in the sense when making investment decisions the preference relation of the investor satisfies all the axioms of choice. Research in behavioural science indicates that investment related decis...

The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on the binomial tree model and options with specific payoffs such as calls or puts, often under certain bo...