This paper deals with the determination of the classical risk probability associated with the compound Poisson process in a small support space. In this paper, we determine a measure α^* of an M small support subspace in which we evaluated the ruin probability. This M subspace is considered here as the space in which the best approximation of the f distribution of claims is zero. We considered two cases for the distributions of total claims amount, namely the α-stable distribution and the symmetric α-stable distribution.  From these considerations, we are able to evaluate α^* and the corresponding ruin probabilities.

best approximation, subspace measure, stable distribution, ruin probability, compound Poisson risk, risk model, renewal equation.