Finite Time Ruin Probability with Constant Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equation U_n = U_n-1(1 + r) - X_n for n ≥ 1, where, U₀ = x ≥ 0 is the initial surplus, r > 0 is the constant interest rate, each X_n denotes the gross loss during the nth year, and X_n, n = 1, 2, ..., constitute a sequence of i.i.d. real valued r.v.´s with common d.f. F. This paper investigates the ruin probability within a finite horizon and obtains a simple and uniform asymptotic relation when the claimsize is of extended regular variation.