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Improvement of No Claim Discount System in Automobile Insurance
Author: DengXingLing
Tutor: LiHengZuo
School: Southwestern University of Finance and Economics
Course: Insurance
Keywords: NCD system The number of claims The amount claimed Superimposed distribution Open markets Information platform
CLC: F426.471
Type: Master's thesis
Year: 2010
Downloads: 157
Quote: 2
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Abstract
In property insurance, auto insurance account for a large proportion of the operating conditions of the car insurance direct impact on the healthy development of the commercial property and casualty insurance company profits and property insurance market. Automobile insurance is one of the modern insurance industry insurance, auto insurance, whether it is in the insurance industry developed Western countries, the insurance industry is relatively backward country occupies a very important position in the whole field of property and casualty insurance business. Auto insurance system of rewards and punishments (BonusMalus System, referred to as BMS) is widely used in the world an experience of the insurance company estimated fee system is mainly based on the driver's historical claims records to determine their renewal premiums. In China, various insurance companies have formulated their own incentive system or NCD (No Claim Discount System, referred to as the NCD system). NCD system enables each policyholder to pay premiums more truly close to the individual risk; reduced to some extent due to moral hazard losses caused to the insurer; encourage the insured to drive carefully; can reduce the micro the occurrence of claims. However, the current NCD system, there are some issues to be resolved: (1) how to improve the fitting accuracy of the loss of data. In the fitting of the loss distribution model, actuaries are most concerned about is the right tail of the distribution (ie, amount of claim losses), because of the emergence of these high losses will seriously affect the financial balance of the insurance company, however, the right tail of the data are often is the least, so fitting in the left tail (small losses) may have a higher credibility, but in the right tail of the effect may not be so. (2) how the introduction of the amount claimed in the NCD system. Most of the existing NCD system only takes into account the number of claims, without taking into account the size of the claim. This the existing NCD system does not make full use of the insured risk. (3) the existing NCD systems are assumed in the closed market environment, and the fact that we are facing is open access policy environment. (4) the industry establish a comprehensive information platform of auto insurance policyholders data. All NCD system analysis are based on the insured is always in the NCD system information between insurance companies closed, highrisk policyholders can in order to escape punishment, for an insurance company, we discuss no claim discount system becomes ineffective. So, the NCD system for further research and improvement, contribute to the accurate pricing of motor vehicle insurance to improve valuation levels and the healthy development of the property and casualty insurance market in China. This paper is divided into a total of five parts, the proposed insurance, nonlife actuarial science, mathematics, statistics, and other disciplines relevant theoretical knowledge the NCD system as the main line to do the detailed analysis of the system, and solve the above problem NCD system improvements and empirical analysis (empirical data all come from a property and casualty insurance company in southwest excited for the year 2008 vehicle claim size data). Chapter 1, Introduction. Introduces the purpose and significance of this study, the research status and development trend of research ideas and research methods, the study of innovation and shortcomings. Analysis of the current system for NCD research status, and pointed out the inadequacies of the study proposed the need for further research and improvement continue to NCD system. Chapter II, NCD system basis. First introduced the P \u0026 C rates determined by the general principles and methods; Second, we introduced the NCD system uses the basic mathematical tools, car insurance no claim discount system is studied theoretically, using Markov chain modeling and a stable analysis, come to the conclusion there any stationary distribution. This chapter is mainly for the later chapters lay the theoretical foundation, directly behind the conclusion of this chapter. Chapter III, the optimal single factor NCD system  based on the number of claims no claim discount system. This chapter begins with a brief introduction to a few number of claims distribution model, divided into homogeneous and nonhomogeneous, focus on the end of the chapter two  NCD theoretical model and application model based on the number of claims to number of claims distribution model, selected through empirical analysis which fit relatively good effect model: negative binomial model and bivariate distribution model for superimposed intends to arrive at a closer the actual fitting model, the data closer to the tail actual value shown superimposed distribution of data fitting results better. Thus, for insurance companies to develop a more reasonable insurance pricing to provide better material; no claim preferential treatment based on the number of claims of systematic theoretical model, this paper has studied the three main models: expectations principle no claim discount system, under the principle of zero utility NCD system and to consider prior information no claim discount system, which in turn on the previous model has been improved; in the last part of the model based on the number of claims NCD us a brief analysis a basic model. Chapter optimal twofactor NCD system  based on the amount claimed no claim discount system. This chapter is a focus of this thesis, we analyzed the NCD system based on the number of claims in the third chapter. Such NCD system there are many deficiencies in recent years, many actuaries begin taking into account the number of claims and claim size no claim discount system. Consolidated results of the literature, the first section of this chapter, first a brief introduction several commonly claim amount distribution model, focusing on the end of the chapter two  the theoretical model and application model based on the amount claimed no claim discount system use to the distribution model, selected through empirical analysis which intends to effect a better model: lognormal distribution, and then superposition of several commonly used distribution fitting, to arrive at a more close to the actual fitting model, the tail data closer to the actual value, shown superimposed on the distribution of the amount claimed is data fitting with better results; Then we focus on analysis of two types of the NCD system theory to consider the size of the claim model; given no claim discount system to consider the size of the claim in theoretical research has been a great breakthrough, but the application of the promotion, popularization needed too much research, at the end of the chapter one, we try to factor into the amount claimed the reward and punishment system, consider the size of the claim application model to establish a and an application model for analysis, including the transfer matrix, stable distribution, the determination of the level of premiums Finally, a property and casualty insurance company of China's southwest excited for the year 2008 vehicle claims the size of the data given in the empirical analysis. Chapter V of the model improvements and suggestions. This chapter is a focus of this article. The incentive system is closed markets or policy portfolio, and we are faced with in real life policyholders in and out of an open environment. In the first section of this chapter, we will be in an open environment is given each level the number of policies in force model based on the limit distribution of open market incentive system level. And delay differential equations constructed incentive system in the open market in the assumption of an open market environment, the number and scale model of each grade of each class of policyholders leaving and entering the system rate and delay factors satisfy certain conditions, We use fixed point theorem and differential inequality method to prove the existence of a unique stationary distribution and global exponential stability, and Finally, the empirical analysis. NCD system all of the above analysis are based on the insured is always in the NCD system, if the insurance company closed between highrisk policyholders can in order to escape punishment, for an insurance company so We discussed NCD system becomes ineffective. In order to avoid this from happening. I propose the establishment of auto insurance information sharing platform, and pointed out the importance of the platform to build. The innovation of this paper is mainly manifested in: (1) the use of a property and casualty insurance company of the southwest excited for the year 2008 vehicle claims the size of the data model and theory throughout the empirical analysis. (2) is established considering the amounts claimed the size of the model and the empirical analysis. (3) the introduction of the policy in and out of an open environment, modeling and empirical analysis.

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