需求影响下财产保险的多目标定价问题研究

Multi-objective Pricing of Property & Casualty Insurance Product with the Influence of Demand

保险产品的定价问题涉及多个利益主体,需要满足多个目标,具有多目标属性。价格除了影响保费收入,还影响到保险公司的资本投入、资本运用等多个决策环节。同时,在定价研究中,需求对价格的影响也不可忽略。为了解决不同利益主体以及不同目标之间的矛盾冲突性,本文建立了多目标定价模型,在约束条件下考察同时追求价值最大化和承保利润最大化的保险人如何决定最优的产品价格和资本投入。同时,本文的研究在期权定价方法的基础上,引入消费者需求函数,对需求影响下财产保险的多目标定价问题进行深入研究。结果显示,相对于单目标模型的部分不足,如利润最大化模型对资本的高需求,价值最大化模型对违约风险的低要求,多目标模型能够兼顾多个发展目标,并且可以根据不同发展阶段的不同需求,进行灵活经营管理。

Pricing of Property Casualty insurance product is related to multiple stakeholders,including stockholders,managers,customers and regulators.The expectation of insurance price varies among different stakeholders.Firstly,for stakeholders,they expect a price which can enhance the profitability of insurance company without harming the enthusiasm of sellers.Secondly,the expectation of managers is complicated.They change their expectation for different products according to the design objectives.Thirdly,for customers,they use insurance products to protect themselves against risks.Therefore,they pay special attention to the default risk of insurance products.Lastly,for regulators,they hope the price to be fair and reasonable.As a consequence,the pricing decision is not isolated.Instead,it have to balance the interests of all stakeholders.In other words,pricing decision has multi-objective features.The features of multi-objective require insurance company to consider multi objectives when making pricing decisions.The first important goal is to maximize company＇s value.Another equally important goal is to maximize the security of insurance company.The last one is to maximize profit as is often used in economics.Meanwhile,the company is always under dynamic developing process.Total premium income is not the only factor which is directly related to price.Initial capital contribution and capital allocation are also influenced by product price.Therefore,a multi-objective pricing model is necessary to balance different goals and solve several problems at the same time.As a normal product,the demand of insurance product submits to the law of demand,which is the price of a normal product is inversely related to demand of the product without changing the other conditions.While the tradition pricing method seldom took demand into the consideration,which went against the demand law.In addition,theoretically and empirically studies have proved that the awareness of default risk has an influence on consumers＇ insurance purchase behavior and insurance demand is very sensitive to the insurer＇s level of default risk.Therefore both price and default risk are important factors when considering insurance demand.Based on the considerations,we build a multi-objective pricing model with the goals of value maximization（which is denoted by EVA） and expected underwriting profit maximization.Both price variable and initial capital variable need to be solved in this model.linear demand function is assumed to be a function of price and default option.Value of default option is obtained under the equivalent martingale measure.Because of the non-linear relationship between price and default option,numerical techniques are required in order to determine the optimal capitalization and price.A direct search method is used to maximize EVA and expected underwriting profit.Different initial points are given and the process is repeated thousands of times to ensure the objective function converged to a global maximum.Findings demonstrate that multi-objective pricing model is better that single-objective pricing model.Instead of high demand of initial capital for profit maximization model and high insolvency risk under value maximization model,our model provide a balance between capital and risk.The influence of various parameters of the demand function are analyzed numerically afterwards.The results show that the optimal prices are more sensitive to the price elasticity of demand while the optimal capital are more depended on the influence of default option.By the end of our study,frictional costs including capital costs and corporate tax are analyzed.We find that the influence of frictional costs on optimal price is trivial but optimal capitalization is largely reduced.Compare to adjusting price to reduce risk,insurer prefer to use capital strategy as the most useful risk management tool.Therefore,our study provide useful findings in pricing decision and risk management for insurance company.