On Erlang(2) risk process perturbed by diffusion

Kam C. Yuen, Hailiang Yang, Rongming Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In thi s article, we consider an Erlang(2) risk process perturbed by diffusion. From the extreme value distribution of Brownian motion with drift and the renewal theory, we show that the survival probability satisfies an integral equation. We then give the bounds for the ultimate ruin probability and the ruin probability caused by claim. By introducing a random walk associated with the proposed risk process, we define an adjustment-coefficient. The relation between the adjustment-coefficient and the bound is given and the Lundberg-type inequality for the bound is obtained. Also, a formula of Pollaczek-Khinchin type for the bound is derived. Using these results, the bound can be calculated when claim sizes are exponentially distributed.

Original languageEnglish
Pages (from-to)2197-2208
Number of pages12
JournalCommunications in Statistics - Theory and Methods
Issue number11
Publication statusPublished - 2005
Externally publishedYes


  • Adjustment-coefficient
  • Brownian motion with drift
  • Diffusion
  • Erlang(2) risk process
  • Integral equation
  • Lundberg's inequality
  • Martingale
  • Random walk


Dive into the research topics of 'On Erlang(2) risk process perturbed by diffusion'. Together they form a unique fingerprint.

Cite this