De Vylder and Goovaerts' conjecture on homogeneous risk models with equalized claim amounts

Bara Kim, Jeongsim Kim, Jerim Kim

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

De Vylder and Goovaerts (2000) made a conjecture on the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability in an associated model with equalized claim amounts. The conjecture, however, remains an open problem. In this paper, we provide a conjecture that is stronger than De Vylder and Goovaerts' conjecture and also provide sufficient conditions for the conjectures, which are more mathematically tractable than De Vylder and Goovaerts' conjecture and thus easier to work with. By using the sufficient conditions for the conjectures, we solve De Vylder and Goovaerts' conjecture when n=3, where n is the number of claims in the finite time.

Original languageEnglish
Pages (from-to)186-201
Number of pages16
JournalInsurance: Mathematics and Economics
Volume101
DOIs
Publication statusPublished - 2021 Nov

Bibliographical note

Funding Information:
We are grateful to the reviewers for their valuable comments and suggestions. The first author's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1A2B5B01001864 ). The second author's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1F1A1A01065568 ). The third author's research was supported by the Basic study and Urban convergence R&D research fund of the University of Seoul ( 2019 ).

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

  • De Vylder and Goovaerts' conjecture
  • Homogeneous risk model
  • Order statistics
  • Risk reserve process
  • Ruin probability

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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