Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model

In this paper, we prove recursive formulas for ultimate time survival probability when three random claims X, Y, Z in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time t 2 f1, 2,...g, claim Y additionally occurs at even moments of time t 2 f2, 4,... g and claim Z additionally occurs at every moment of time, which is a multiple of three t 2 f3, 6,... g. Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form fX, X + Y, X + Z, X + Y, X, X + Y + Z,...g. Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples.