Multiseasonal discrete-time risk model revisited

In this work, we set up the distribution function of M := sup(n >= 1) Sigma(n)(i=1) (X-i - 1), where the random walk Sigma(n)(i=1) X-i, n is an element of N, is generated by N periodically occurring distributions, and the integer-valued and nonnegative random variables X-1, X-2, ... are independent. The considered random walk generates a so-called multiseasonal discrete-time risk model, and a known distribution of random variable M enables us to calculate the ultimate time ruin or survival probability. Verifying obtained theoretical statements, we demonstrate several computational examples for survival probability P(M < u) when N = 2,3, or 10.