In this paper, we consider a renewal risk process with negative
risk sums. We derive integral equations and integro-differential
equations for the survival and ruin probabilities for the proposed
model. Exact expression and upper and lower bounds for the
ruin probability are obtained. We also present some closed form
expressions for the survival and ruin probabilities under some
certain choices of the claim amount distribution and the distribution of the
inter-occurrence time of the claims.