Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al.(2010), the price process of the investment portfolio is described as a geometric L′evy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al.(2010).
The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
