A new aspect of a risk process and its statistical inference

Yasutaka Shimizu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the process does not necessarily correspond to the each claim size. Therefore our risk process is different from the traditional risk process. We cannot directly observe each jump size because of discrete observations. Our goal is to estimate the adjustment coefficient of our risk process from discrete observations.

Original languageEnglish
Pages (from-to)70-77
Number of pages8
JournalInsurance: Mathematics and Economics
Issue number1
Publication statusPublished - 2009 Feb
Externally publishedYes


  • Adjustment coefficients
  • Diffusion perturbations
  • Discrete observations
  • Risk process
  • Statistical inference

ASJC Scopus subject areas

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


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