Remarks on a generalized inverse Gaussian type integral with applications

作者：

Highlights：

• Study a generalized Esscher transform of the generalized inverse Gaussian distribution.

• Develop an explicit expression for the cumulative distribution function of the GIG with a half-integer parameter which was unknown in the literature.

• Apply some applications to the mixed Poisson with the truncated GIG-type distribution, TVaR and the finite-time ruin probability for a Sparre Andersen work models are provided.

摘要

•Study a generalized Esscher transform of the generalized inverse Gaussian distribution.•Develop an explicit expression for the cumulative distribution function of the GIG with a half-integer parameter which was unknown in the literature.•Apply some applications to the mixed Poisson with the truncated GIG-type distribution, TVaR and the finite-time ruin probability for a Sparre Andersen work models are provided.

论文关键词：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

论文评审过程：Received 12 January 2022, Revised 26 May 2022, Accepted 4 June 2022, Available online 10 June 2022, Version of Record 10 June 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127302