Improved asymptotic upper bounds on the ruin capital in the Lundberg model of risk

This paper deals with ruin capital uα,t(c∣λ,μ) in the classical Lundberg model of risk. It is defined as the initial capital needed to keep the probability of ruin within finite time t equal to a predefined value α. Considered as a decreasing function of premium rate c, the ruin capital is shown to be convex (i.e., concave downward) for c>λ/μ and t sufficiently large. This observation is used to construct explicit upper bounds on the ruin capital.