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Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 348–354 | Cite as

On the Discounted Kth Moment of the Deficit at Ruin in the Delayed Renewal Risk Model

  • So-Yeun Kim
  • Bangwon Ko
Article
  • 16 Downloads

Abstract

In this paper, we derive a very general expression for the discounted kth moment of the deficit at ruin in the delayed renewal risk model. The formula would yield some of the earlier relevant results as special cases, and reduce to a mathematically tractable form if the distributions for claim sizes and interclaim times are of exponential variants including a mixture of Erlang distributions. We provide numerical examples with an emphasis on the impact of the time until the first claim on the kth moment of the deficit at ruin.

Keywords

Deficit at Ruin Delayed Renewal Risk Model Gerber–Shiu Function Time of Ruin 

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References

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Finance and InsuranceHongik UniversitySejongKorea
  2. 2.Department of Statistics and Actuarial ScienceSoongsil UniversitySeoulKorea

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