Gerber, H.U. (1970) An Extension of the Renewal Equation and Its Application in the Collective Theory of Risk. Skandinavisk Aktuarietidskrift, 1970, 205-210.

has been cited by the following article:

• TITLE: Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals

  AUTHORS: Heli Gao

  KEYWORDS: Jump-Diffusion Risk Process, Diffusion, Geometric Brownian Motion, Gerber-Shiu Function

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.11, November 22, 2016

  ABSTRACT: The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.