This paper presents mathematical formulation for the probability distribution function of asset value difference using canonical ensemble framework. For asset value significantly smaller than the total market value, the distribution is given by exponential function, which depends on market-eta...

This paper presents a unified framework for the popular Skewed Generalized t (SGT) distribution and its special cases the Skewed Generalized Error Distribution (SGED), the skewed student's t, the skewed Laplace and skewed normal distributions. The analytical moment equations presented can be...

In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one,...

Mixed exponential distributions are frequently used in actuarial risk modeling. Distributions obtained through mixtures allow greater flexibility in the modeling of non-life insurance loss amounts . Several research works have studied mixed exponential distributions in univariate and...

In a one-step trinary lying experiment, subjects privately observe a random device that indicates a low payoff, an intermediate payoff or a high payoff. Subjects are paid whatever they report, inducing some subjects to lie in order to receive a higher payoff. This paper presents a methodology...

Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of the mean value of functional $p$-norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we...

The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density f(x)~f_0 x^(-2), with the coefficient depending on the means and variances of the numerator and denominator, and their correlation. We also obtain the conditional...

This paper studies in detail simulation methods for simulating tail probability and tail mean of both univariate and bivariate compound variables. We first reviewed some basic variance reduction methods, then we proposed several novel combinations of variance reduction methods specifically for...