Zero-capital survival probability
= Zero-capital survival probability
{title2=$\varphi(0)=1-\lambda\mu/c$}
In a <classical risk model> with positive <relative safety loading>, zero initial capital has ultimate <survival probability> $1-\lambda\mu/c$, where $\lambda$ is the claim-arrival rate, $\mu$ the claim <expected value> and $c$ the premium rate. It depends on the claim law through its mean alone. It is not the event of never receiving a claim: premium accumulates between arrivals.