Asymptotic Normality of Nonparametric Estimate for Zero-Utility Premiums

Zero-utility principle is one of the main premium pricing principles, which has been widely used in insurance practice. In this paper, the nonparametric estimation of zero-utility premium is given. In addition, the consistency and asymptotic normality of the estimation are proved. Some special cases including linear, exponential and quadratic utility are discussed. Finally, the Monte Carlo method is used to show the convergence rate of premium estimation. Furthermore, the histogram and Normal-Probability-Plot are given to investigate the asymptotic normality of the estimators. The results show that our estimations are good enough to use in practice.