Let ψ(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ψ(u) behaves asymptitically like a multiple of exp(¸-Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper the authors deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. They show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. The authors also give the results of simulation study that compares the different techniques in some particular cases.
