Ultimate ruin probability
= Ultimate ruin probability
{title2=$\psi(u)=\mathbb P(\inf_{t\ge0}U_t<0)$}
The probability that the insurance surplus in a <classical risk model> becomes negative at some finite time, starting from capital $u\ge0$. Ultimate survival has probability $1-\psi(u)$. A finite-horizon ruin probability instead restricts the crossing time to a specified time interval.