EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE

摘要

In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Φ_δ(u,w) are discussed, the Feller expression and the integro-differential equation satisfied by Φ_δ(u,w) are derived. Finally, the decomposition of Φ_δ(u,w) is discussed, and some properties of each decomposed part of Φ_δ(u,w) are obtained. The results can be reduced to some ones in Gerber and Landry's, Tsai and Willmot's, and Wang's works by letting parameter δ and (or) σ be zero.