Summary: We deal with a risk process with reinsurance which is a generalization of the classical risk process. We propose upper and the lower estimates for \(e^{x\alpha}r(x)\) provided that \(\alpha\) is known, but \(r(x)\) is defined by the equation \(q(u)=\int_u^{\infty}r(s)ds\), where \(q(u)\) is the ruin probability.