The classical ruin problem on a finite solvable group

Abstract

For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, “from” a fixed subset, to obtain a new proof of the well-known formula which allows one to estimate the characteristic function of the ruin probability (hitting the identity of a group) at the th- trial.