Compound Poisson models with completely monotone claim sizes

Question

Assume that the free surplus of an insurance company at time t is modeled by \begin{equation} R(t)=u+ct-\sum_{k=1}^{N(t)}X_k \end{equation} where u is the initial surplus, the stochastic process N(t) denotes the number of claims up to time t and the random variables $X_k$ refer to the corresponding claim amounts.\ Here $c > 0$ is a constant premium intensity and $u\geq 0$ is the initial surplus in the portfolio. The classical Cramer-Lundberg risk model assumes that ´ N(t) is a homogeneous Poisson process with intensity $\lambda$, which is independent of the claim sizes and the claim sizes are independent and identically distributed. Under this assumption, various quantities can be calculated explicitly for certain classes of claim size distributions, including the probability of ruin \begin{equation} \psi(u)=Pr(R(t)<0 for some t>0). \end{equation} . my question is why if $\psi_\theta(u)$ denote the ruin probability of the classical compound Poisson risk model with independent Exp($\theta$) claim amounts then \begin{equation} \psi_\theta(u)=\min(\frac{\lambda}{\theta c}\exp\{ -(\theta - \frac{\lambda}{c}) \},1) \end{equation} ??