a Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
b Department of Mathematics, Qufu Normal University, Shandong, People's Republic of China
Abstract:
This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts–Schmidli model are derived.