Approximations for moments of deficit at ruin with exponential and subexponential claims

Abstract

Consider a renewal insurance risk model with initial surplus u>0 and let A u denote the deficit at the time of ruin. This paper investigates the asymptotic behavior of the moments of A u as u tends to infinity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the φ-moments of A u , where φ is a non-negative and non-decreasing function satisfying certain conditions.