Upper bounds for ruin probabilities in the Sparre Andersen model

We consider the problem of estimating the adjustment coefficient R in the Sparre Andersen model, which allows us to estimate upper bounds for the ruin probability of insurance companies. We propose a consistent estimator for R and establish a result about its asymptotic normality. Moreover, we show that it is possible to construct confidence intervals for R based on that estimator, using the tail bootstrap procedure. We also compare the confidence intervals computed using the normal approximations and the tail bootstrap method. We present the results of a simulation study in some particular cases.