On the ruin problems for a Cox risk process

In this article we study a Cox risk process taking both risk and portfolio fluctuations into account. Using the stochastic operational time scale, we show that the Gerber-Shiu function in the Cox risk model can be expressed in terms of the joint density of the ruin time, the surplus before ruin and the deficit at ruin in the compound Poisson risk model and the Laplace transform of the intensity measure. We also obtain explicit expressions for the Gerber-Shiu function under some useful choices of the intensity process.