We analyze the classical Brownian risk models discussing the approxima-
tion of ruin probabilities (classical, γ-reflected, Parisian and cumulative
Parisian) for the case that ruin can occur only on specific discrete grids. A
practical and natural grid of points is for instance G(1) = {0,1,2,...}, which
allows us to study the probability of the ruin on the first day, second day,
and so one. For such a discrete setting, there are no explicit formulas for the
ruin probabilities mentioned above. In this contribution we derive accurate
approximations of ruin probabilities for uniform grids by letting the initial
capital to grow to infinity.