Bayesian Prediction And Statistical Analysis Of Risk Premium In Insurance Actuarial Science

The premium(insurance premium)is a fixed fee paid by the policy holder in order to transfer the uncertainty loss of the insurance subject to insurance company.For insurance companies,it is one of the important tasks of an actuary to determine an appropriate premium for a policy and to estimate premiums through various kinds of information.Since premiums often rely on the risk characteristics of the insurance subject,and the combination of these risk characteristics is generally characterized by a risk parameter B.Due to the non-homogeneity of risk,risk parameter? is generally considered as random variables with some prior distribution.Therefore,the estimation of premiums falls into the Bayesian framework.Premiums that depend on risk parameters at this time are called risk premiums.Since risk parameter is a random variable which is not observable,and need to be estimated based on available information.This paper researched the Bayesian estimation of risk premiums under some commonly used premium principles in non-life insurance science.In the second chapter,we propose the principle of moment-related premiums by combining the principle of net premiums,principle of expectation,principles of variance,principles of standard error,etc.,and then studied the Bayesian estimation of risk premiums in the principle of moment-related premiums.The large-sample property of the estimation is proved and the convergence speed of the estimartion is verified.In Chapter 3,the Bayesian prediction and Bayesian estimation of the risk premium under the Esscher premium principle are studied.Since the Esscher premium principle corresponds to the exponentially weighted loss function.Therefore,the risk premiums and Bayesian premiums are defined by minimizing expected losses under this loss function.Examples are used to illustrate various calculation methods for premiums and Bayesian estimation;Chapter IV studies the estimation of risk premiums under the exponential principle.The Bayesian estimate and Bayesian premium for risk premium under the exponential principle are obtained,and the statistical properties of the estimate are proved.The mean square error of each estimate is compared using numerical simulation method.Chapter 5 studies the Over-dispersion Poisson model for multiple contracts.The Bayesian method is used to study the Bayesian estimation and Bayesian prediction of risk parameters.The empirical Bayesian method is used to estimate the structural parameters and the properties of the estimation are discussed.An empirical Bayesian estimate of risk parameters is obtained.Finally,the effectiveness of the estimation is verified by numerical simulation.Finally,the paper summarizes the full text and proposes further research directions.