Let psi(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 psi(u) behaves asymptotically like a multi
ple of exp(-Ru) where R is the adjustment coefficient; R depends on th
e premium income rate, the claim size distribution and the distributio
n of the time between claim arrivals. Estimation of R has been conside
red by many authors. In the present paper we deal with confidence boun
ds for R. A variety of methods is used, including jackknife estimation
of asymptotic variances and the bootstrap. We show that, under certai
n assumptions, these procedures result in interval estimates that have
asymptotically the correct coverage probabilities. We also give the r
esults of a simulation study that compares the different techniques in
some particular cases.