CONFIDENCE-BOUNDS FOR THE ADJUSTMENT COEFFICIENT

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.