We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.
- Lévy risk process
- discrete observations
- expected discounted penalty function
- regularized Laplace inversion
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty