Ruin probability in the three-seasonal discrete-time risk model

This paper deals with the discrete-time risk model with nonidentically distributed claims. We suppose that the claims repeat with time periods of three units, that is, claim distributions coincide at times $\{1,4,7,\dots \}$, at times $\{2,5,8,\dots \}$, and at times $\{3,6,9,\dots \}$. We present the recursive formulas to calculate the finite-time and ultimate ruin probabilities. We illustrate the theoretical results by several numerical examples.