  In this work we set up the distribution function of
$\mathcal{M}:=\sup_{n\geqslant1}\sum_{i=1}^{n}{(Z_i-1)}$, where the random walk
$\sum_{i=1}^{n}Z_i, n\in\mathbb{N},$ is generated by $N$ periodically occurring
distributions and the integer-valued and non-negative random variables
$Z_1,\,Z_2,\,\ldots$ are independent. The considered random walk generates
so-called multi seasonal discrete time risk model, and a known distribution of
random variable $\mathcal{M}$ enables to calculate ultimate time ruin or
survival probability. Verifying obtained theoretical statements we demonstrate
several computational examples for survival probability
$\mathbb{P}(\mathcal{M}< u)$ when $N=2,\,3$ or $10$.
