A state-dependent dual risk model

Abstract

In a dual risk model, the premiums are considered as the costs and the claims are regarded as the profits. The surplus can be interpreted as the wealth of a venture capital, whose profits depend on research and development. In most of the existing literature of dual risk models, the profits follow the compound Poisson model and the cost is constant. In this paper, we develop a state-dependent dual risk model, in which the arrival rate of the profits and the costs depend on the current state of the wealth process. Ruin probabilities are obtained in closed-forms. Further properties and results will also be discussed.