Remarks on a generalized inverse Gaussian type integral with applications

Gordon E. Willmot and Jae-Kyung Woo

Applied Mathematics and Computation, 2022, vol. 430, issue C

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.

Keywords: Truncated inverse gaussian; Generalized inverse gaussian cumulative distribution function; Size-biased Esscher transform; Mixed Poisson distribution; Tail value-at-Risk (TVaR); Finite-time ruin probabilities (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003769

DOI: 10.1016/j.amc.2022.127302

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