DeepAI AI Chat
Log In Sign Up

Keep It Real: Tail Probabilities of Compound Heavy-Tailed Distributions

by   Igor Halperin, et al.

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly convergent one-dimensional integral involving a discontinuity of the imaginary part of its moment generating function across a branch cut. The latter integral can be evaluated in quadratures, or alternatively represented as an asymptotic expansion. Our approach thus offers a viable (especially at high percentile levels) alternative to more standard methods such as Monte Carlo or the Fast Fourier Transform, traditionally used for such problems. As a practical application, we use our method to compute the operational Value at Risk (VAR) of a financial institution, where individual losses are modeled as spliced distributions whose large loss components are given by power-law or lognormal distributions. Finally, we briefly discuss extensions of the present formalism for calculation of tail probabilities of compound distributions made of compound distributions with heavy tails.


page 1

page 2

page 3

page 4


Fourier transform MCMC, heavy tailed distributions and geometric ergodicity

Markov Chain Monte Carlo methods become increasingly popular in applied ...

Asymptotic distributions for weighted power sums of extreme values

Let X_1,n≤⋯≤ X_n,n be the order statistics of n independent random varia...

On Optimization over Tail Distributions

We investigate the use of optimization to compute bounds for extremal pe...

Approximations to ultimate ruin probabilities with a Wienner process perturbation

In this paper, we adapt the classic Cramér-Lundberg collective risk theo...

Censoring heavy-tail count distributions for parameters estimation with an application to stable distributions

Some families of count distributions do not have a closed form of the pr...

Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions

Generative adversarial networks (GANs) are often billed as "universal di...

Exactly computing the tail of the Poisson-Binomial Distribution

We offer ShiftConvolvePoibin, a fast exact method to compute the tail of...