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We investigate performance of approximations put forth in\citeNP{[Malinovskii 2017a]} and \citeNP{[Malinovskii 2017b]} for thedistribution of the time of first level $u$ crossing by the random process$\homV{s}-cs$, $s>0$, where $\homV{s}$ is compound renewal process. In the caseof Exponential inter-renewal and jump size random variables, we compare theapproximations with exact and with simulation results. In a few other casesincluding Erlang and Pareto inter-renewal and jump size random variables, whereexact results are absent, we compare the approximations with simulationresults.

On approximations for the distribution of first level crossing time