Bonus-Malus Scales' Generalization And Application Of Bonus-Malus Model In Other Fields

Bonus-Malus System is an important research project in modern actuary. In essence, The system is that the insurer asks more premium to the policy holders who had one or more claims in last year,and gives discount to the policy holders who had no claims in last year. And we try our best to get an optimal system in a sense. Form insurance practice,we know that BMS has important theoretical and practical sense. In this paper,we will see that using the relate knowledge about stochastic process,matrix theory and microeconomics, the trajectory of each policyholder can be creatively modeled with the aid of the continuous time Markovian process. At the same time, the Bonus-Malus model is creatively applied to loan businesses of banks by adjusting Bonus-Malus lending rate to reduce loan fraud. The main contents of this paper include:Firstly,we put forward the object of study: Bonus-Malus system, and introduce the basic knowledge of Bonus–Malus system and the innovations of the paper. Meanwhile, we introduce the knowledge of Bonus–Malus scales in brief which is already widely used.Secondly, this paper is devoted to the design of Bonus–Malus scales involving different types of claims which are distinguished from each other and entail different penalties. Bonus–Malus scales are always linked with discrete time Markov chain in insurance before, however, this article develops such fixed thinking, extending discrete time Markov chain to continuous time Markovian process rationally, namely, the trajectory of each policyholder can be modeled with the aid of the continuous time Markovian process. Moreover, the stationary distribution which is needed in Bonus–Malus scales is obtained through speed transfer matrix of Markovian process. And a appropriate numerical example is given, the rationality and feasibility of the theory above will be proved.Thirdly, the Bonus-Malus model is applied to loan businesses of banks by adjusting Bonus-Malus lending rate to reduce loan fraud. The main idea is to establish personal bank credit system of borrower's and fix borrower's repayment rate of next stage through his present performance and repayment rate. Then a kind of incentive mechanism is presented, which is different from the complete audit mechanism. Under some simple assumptions, it can be proved that Bonus-Malus interest rate would eliminate all fraud, rather than simply reduce it.Finally, we make a summary and a concise announcement of the deficiency in it and draw out the problem worthy to be studied in later research.