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...

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...

We introduce the new F-Riesz distribution to model tail-heterogeneity in fat-tailed covariance matrix observations. In contrast to the typical matrix-valued distributions from the econometric literature, the F-Riesz distribution allows for di↵erent tail behavior across all variables in the...

There has been much work on the approximation of independent or dependent random variables. But we are not aware of any work giving exact results for the approximation of the sum of randomly weighted random variables. In this paper, we derive results for the randomly weighted sum of dependent...

Stochastically ordered random variables with given marginal distributions are combined into a joint distribution preserving the ordering and the marginals using a maximum entropy formulation. A closed-form expression is obtained. An application is in default estimation for different portfolio...