Non-parametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model

作者：Shimizu Yasutaka^*

来源：Scandinavian Actuarial Journal, 2012, 2012(1): 56-69.

DOI：10.1080/03461238.2010.523515

• Risk model perturbed by diffusions
• The expected discounted penalty function
• Laplace transform
• Empirical estimator
• Regularized inversion

A non-parametric estimator of the Gerber-Shiu function is proposed for a risk process with a compound Poisson claim process plus a diffusion perturbation; the Wiener-Poisson risk model. The estimator is based on a regularized inversion of an empirical-type estimator of the Laplace transform of the Gerber-Shiu function. We show the weak consistency of the estimator in the sense of an integrated squared error with the rate of convergence.

• 出版日期2012