Remarks on a generalized inverse Gaussian type integral with applications

Abstract

In this paper, we consider the truncated Inverse Gaussian (IG) distribution and the generalized Inverse Gaussian (GIG) distribution and then obtain the components in its generalized Esscher transform and size-biased Esscher transform. Consequently, this enables us to derive an explicit expression for the cumulative distribution function of the GIG distribution with a half-integer parameter. We show that this result has applications for the evaluation of the mixed Poisson with the truncated GIG-type distribution, Tail Value-at-Risk for GIG risk, and for a Sparre Andersen risk model.