Approximations for moments of de"cit at ruin with exponential and subexponential claims

Consider a renewal insurance risk model with initial surplus u ¿0 and let Au denote the de"cit at the
time ofruin. This paper investigates the asymptotic behavior ofthe moments of Au as u tends to in"nity.
Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some
asymptotic relationships for the -moments of Au, where is a non-negative and non-decreasing function
satisfying certain conditions.