  In this paper a quantitative analysis of the ruin probability in finite time
of discrete risk process with proportional reinsurance and investment of
finance surplus is focused on. It is assumed that the total loss on a unit
interval has a light-tailed distribution -- exponential distribution and a
heavy-tailed distribution -- Pareto distribution. The ruin probability for
finite-horizon 5 and 10 was determined from recurrence equations. Moreover for
exponential distribution the upper bound of ruin probability by Lundberg
adjustment coefficient is given. For Pareto distribution the adjustment
coefficient does not exist, hence an asymptotic approximation of the ruin
probability if an initial capital tends to infinity is given. Obtained
numerical results are given as tables and they are illustrated as graphs.
