THE RISK MODEL OF THE EXPECTED DISCOUNTED PENALTY FUNCTION WITH CONSTANT INTEREST FORCE

In this article, the expected discounted penalty function Φδ,α(u) with constant interest δ and “discounted factor” exp(-αTδ) is considered. As a result, the integral equation of Φδ,α(u) is derived and an exact solution for Φδ,α(0) is found. The relation between the joint density of the surplus immediately prior to ruin, and the deficit at ruin and the density of the surplus immediately prior to ruin is then obtained based on analytical methods.