Bounds for classical ruin probabilities (Q799061)

This paper derives upper and lower bounds for the ruin probability over infinite time. The key observation is that if \(u=k*(1-u),\) then \(v-u=(v- k*(1-v))*(1-u),\) where \((f*g)(x)=\int^{x}_{0}f(x-y)dg(y)\). Applications to sub-exponential distributions are also given.