On a Joint Distribution for a Cox Risk Model

In this paper, we consider a Cox risk process taking both risk and portfolio fluctuations into account. Using the stochastic operational time scale, it is shown that the joint distribution of three actuarial diagnostics: the time of ruin, the surplus immediately before ruin and the deficit at ruin in the Cox risk model can be expressed in terms of a joint distribution in the compound Poisson risk model and the density of the intensity measure. We also obtain some distributions of the so-called intensity measure of Cox process related to the model.