The proportional hazard premium of an insured risk \(X\) of distribution function \(F\) depends on the hazard function \(S:=1-F\) and a parameter \(\rho\geq1\), called risk aversion index. This article deals with the estimation of a premium for a given retention level \(R>0\), notation \(\Pi_{\rho,R}\), that is, a reinsurance premium of the high layer \([R,\infty)\). Let us consider a stop-loss contract, where the insurer and the reinsurer retain respectively \(\min(X,R)\) and \(\max(0,X-R)\) (with \(R>0\), the reinsurance retention level of the risk \(X\)). Then the corresponding proportional hazard premium of loss of a high layer is defined by \(\Pi_{\rho,R}:=\int_{R}^{\infty}\{S(u)\}^{1/\rho}\,du\). Let an optimal retention level be defined by \(R_{opt}=F^{\leftarrow}(1-\delta_{opt})\), where \(\delta_{opt}\) is a small enough real number. Here \(F^{\leftarrow}(s):=\inf\{t>0, F(t)\geq s\}\), \(0<t<1\). For heavy-tailed claim amounts a semi-parametric estimator for premium \(\Pi_{\rho,R_{opt}}\) is proposed. Its asymptotic normality is established. Confidence bounds for this premium are computed.