This paper studies random vectors X featuring symmetric distributions in that i) the order of the random variables in X does not affect its distribution, or ii) the distribution of X is symmetric at zero. We derive a number of characterization results for such random vectors, thereby connecting...

Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in...

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...

This paper considers the randomly weighted sums generated by some dependent sub-exponential primary random variables and some arbitrarily dependent random weights. To study the randomly weighted sums with infinitely many terms, we establish a Kesten-type upper bound for their tail probabilities...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...

We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates the...

Determining distributions of the functions of random variables is one of the most important problems in statistics and applied mathematics because distributions of functions have wide range of applications in numerous areas in economics, finance, risk management, science, and others. However,...

Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y=X1X2...

The problem of determining distributions of the product of random variables is one of the most important problems. However, most studies only focus on independence structures on some common distributions of the functions of random variables or stochastic dependence through multivariate normal...

Determining distributions of the functions of random variables is a very important problem with wide applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y = X₁/X ₂ and the...

We consider possible measures of dependence for two symmetric alpha-stable (SαS) random variables. Some results are given which enlighten a few deficiencies of these measures. We propose a new measure which partially solve these problems. The results are illustrated by simulations

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...

This paper presents some new stochastic dominance (SD) criteria for ranking transformations on a random variable, which is the first time that this is done for transformations under the discrete framework. By using the expected utility theory, the authors first propose a sufficient condition for...

Dealing with supply risks is one of the challenges of decision makers in supply chains as producing and sourcing become more and more complex. Theoretical research on different types of supply uncertainty as well as their management is well covered. Behavioral aspects in this context, however,...

This paper proposes a decision-theoretic framework for experiment design. We model experimenters as ambiguity-averse decision-makers, who make trade-offs between subjective expected performance and robustness. This framework accounts for experimenters' preference for randomization, and clarifies...

This paper develops some new stochastic dominance (SD) rules for ranking transformations on a random variable, which is the first time to study ranking approach for transformations on the discrete framework. By using the expected utility theory, the authors first present a sufficient condition...

We revisit the classical problem of convergence of the maximum of cumulative sums of IID random variables by introducing ideas from the Karamata's celebrated proof of the Hardy-Littlewood Tauberian Theorem [J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes,...

Increasingly detailed consumer information makes sophisticated price discrimination possible. At fine levels of aggregation, demand may not obey standard regularity conditions. We propose a new randomized sales mechanism for such environments. Bidders can "buy-it-now" at a posted price, or...

Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the...

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient...

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...

Computers are deterministic devices, and a computer-generated random number is a contradiction in terms. As a result, computer-generated pseudorandom numbers are fraught with peril for the unwary. We summarize much that is known about the most well-known pseudorandom number generators:...

Increasingly detailed consumer information makes sophisticated price discrimination possible. At fine levels of aggregation, demand may not obey standard regularity conditions. We propose a new randomized sales mechanism for such environments. Bidders can "buy-it-now" at a posted price, or...