The Optimal Deductibles On Two Types Of Bonus-malus Systems With Varying Deductibles

The operation mechanism of motor vehicle insurance is to estimate the Bonus-malus levels and the renewal premium of the next policy year through the number of claims and the claim sizes within one policy year.At present,insurance companies in most countries in the world use Bonus-malus systems,and the related issues has been a research focus in insurance theory.This paper studies two types of Bonus-malus systems with varying deductibles,and the optimal allocation schemes for deductibles are obtained.This paper is divided into three chapters:Chapter 1 is an introduction.Firstly,the research background is introduced,Then we present the basic elements of the Bonus-malus systems and the research status at home and abroad.Finally,we give the main results obtained in this article.In chapter 2,we study the single-event Bonus-malus systems with varying deductibles.Firstly,the construction of the model and related assumptions are introduced.Then we investigate the interval estimates of reduced premium proportion and the deductibles.A distribution scheme for the optimal deductibles is given by the severity of the event.Finally,a numerical example is used to explain the theoretical results.In chapter 3,we study the multi-event Bonus-malus systems with varying deductibles.Firstly,the construction of the model and the relevant assumptions are given.The interval estimates of reduced premium proportion and the deductibles are then obtained.A distribution scheme for optimal deductibles is given by a proportion to the average claims.Finally,a numerical example is given.