Ruin Problems for the Discrete Time Risk Model under Stochastic Rates of Interest

The discrete time risk model under stochastic rates of interest is discussed in this paper. The distribution of the sustainable period of ruin, the distribution of surplus immediately when surplus turns back positive, the distribution of supreme surplus before ruin, the joint distribution of surplus before ruin and deficit at ruin and supreme surplus before ruin, the time that the surplus process reach a given level x for the first time are derived in this paper.