Nonparametric estimation of ruin probabilities given a random sample of claims

Abstract

In this paper the well-known insurance ruin problem is reconsidered. The ruin probability is estimated in the case of an unknown claims density, assuming a sample of claims is given. An important step in the construction of the estimator is the application of a regularized version of the inverse of the Laplace transform. A rate of convergence in probability for the integrated squared error (ISE) is derived and a simulation study is included.