It is already known, under certain conditions including stochastic inequalities, the comparison of moments. In this paper, we will study in detail the reverse of this problem, that is, the stochastic orderings implied by moments inequalities. We will limit our study to the absolute value of...

Governments should embrace randomized trials to estimate the efficacy of different laws and regulations. Just as random assignment of treatments is the most powerful method of testing for the causal impact of pharmaceuticals, randomly assigning individuals or firms to different legal rules can...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or more specifically, subexponential random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions, to determine...

In this paper we apply the idea of the WKB method to derive an effective single lognormal approximation for the probability distribution of the sum of two correlated lognormal variables. An approximate probability distribution of the sum is determined in closed form, and illustrative numerical...