satisfies $g\geq 0$, $h\geq 0$, $0 c\}}], \\
E[g(X)\varphi_{1+}^{'}((I(X)-c)_{+})I_{\{I(X)\geq c\}}]&\geq E[h(X)\varphi_{2-}^{'}(X-I(X)+c)],
\end{aligned}
\right.
\end{equation}
where $\varphi_{i-}^{'}$ and $\varphi_{i+}^{'}$ represent the corresponding left and right derivatives of $\varphi_{i}$, $i=1,2$. If $\varphi_{1}$ and $\varphi_{2}$ are strictly convex, the solution is unique. If $\varphi_{1}$ and $\varphi_{2}$ are differentiable and $\varphi'_{1}(0)=\varphi'_{2}(0)=0$, the optimal reinsurance premium…
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