Gerber–Shiu analysis with two-sided acceptable levels

Jae Kyung Woo*, Ran Xu, Hailiang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, insurer's surplus process moved within upper and lower levels is analyzed. To this end, a truncated type of Gerber–Shiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones (e.g. Gerber and Shiu (1998), Cheung et al. (2010a)). A key component in our analysis of this proposed Gerber–Shiu function is the so-called transition kernel. Explicit expressions of the transition function under two different risk models are obtained. These two models are both generalizations of the classical Poisson risk model: (i) the first model provides flexibility in the net premium rate which is dependent on the surplus (such as linear or step function); and (ii) the second model assumes that claims arrive according to a Markovian arrival process (MAP). Finally, we discuss some applications of the truncated Gerber–Shiu function with numerical examples under various scenarios.

Original languageEnglish
Pages (from-to)185-210
Number of pages26
JournalJournal of Computational and Applied Mathematics
Volume321
DOIs
Publication statusPublished - 1 Sept 2017
Externally publishedYes

Keywords

  • Classical Poisson risk model
  • Joint distribution of maximum and minimum before ruin
  • Markovian arrival process
  • Surplus-dependent premium rate
  • Transition kernel
  • Truncated Gerber–Shiu function

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