Ruin problems in risk models with dependent rates of interest

In this paper, we consider ruin problems in two generalized risk models. The effects of timing of payments and interest on the ruin problems in the models are studied. The rates of interest {In,n=1,2,⋯} are assumed to have an autoregressive structure. We obtain the recursive formulas of penalty functions which give a unified treatment to ruin quantities including the distribution of surplus immediately before ruin and the deficit at ruin, etc. Furthermore, we consider the probability properties of the duration of ruin, which are used to describe the severity of ruin.