On the risk of credibility premium rules

Søren Asmussen, Corina Constantinescu, Julie Thøgersen*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

A discrete-time risk process is considered where the full distribution of the claim size X is not completely known to the insurance company. Rather, it assumes that the distribution of X given (Formula presented.) is (Formula presented.) where Z is some structural random variable for which a prior is available. The main emphasis of the paper is the unconditional ruin probability (Formula presented.) in this setting where the premium is either updated according to incoming information about the claim distribution or computed by the expected value principle. This is in turn studied via the conditional ruin probability (Formula presented.), for which large deviations estimates are available. Rigorous proofs are given only for the case of the (Formula presented.) forming a scale parameter family, including the classical case of gamma claims with a gamma prior. However, the analysis readily suggests what should be the behaviour of (Formula presented.) in different models for the claims.

Original languageEnglish
JournalScandinavian Actuarial Journal
Volume2021
Issue10
Pages (from-to)866-889
Number of pages24
ISSN0346-1238
DOIs
Publication statusPublished - 2021

Keywords

  • Conjugate prior
  • credibility premiums
  • gamma distribution
  • large deviations
  • ruin probability
  • scale parameter family

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