Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk objective, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk objective functions i...

Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk objective, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk objective functions i...

Actuarial risks can be analyzed using heavy-tailed distributions, which provide adequate risk assessment. Key indicators, such as value-at-risk, tailed-value-at-risk (conditional tail expectation), tailed-variance, tailed-mean-variance, and mean excess loss function, are commonly used to evaluate exposure levels. In this study, we analyze actuarial these five calculated four different estimatio...

A Cramér-type moderate deviation theorem quantifies the relative error of tail probability approximation. It provides a criterion whether limiting can be used to estimate under study. Chen, Fang and Shao (2013) obtained general result using Stein’s method when was normal distribution. In this paper, theorems are established for nonnormal approximation Stein identity, which is satisfied via exch...