Pricing Of P2P Insurance Based On Prospect Theory And Its Application To Premium Allocation

The P2P insurance model is a new type of insurance model that has emerged in recent years with the penetration of financial technology into the insurance industry.This model relies on the Internet,insuring the insured in the form of a co-insurance group,and drawing premiums into a pool of funds.During the insurance period,the fund pool will be responsible for the payment,and the excess will be paid by the insurance company.After the insurance period ends,the premium will be refunded to the team members according to the remaining situation of the fund pool or the discount for the next year.Its unique co-insurance team formation mechanism uses social networks to subtly transfer people's offline social relationships to online coinsurance groups to generate stronger constraints,which can effectively reduce moral hazard and reduce channel costs.Compared with the traditional insurance company,the P2P insurance model can also refine insurance liability and expand the coverage of insurance liability,which can help traditional insurance companies to carry out special risk business.This model also has a unique premium return mechanism that allows policyholders to receive tangible returns,making insurance companies and policyholders a win-win situation.However,most of the P2P insurance models are still based on the operation of insurance brokers.They cooperate with traditional insurance companies to solve the problem of insufficient ability to develop their own products.As we all know,due to the information asymmetry in the insurance market,how to realize differential pricing is a difficult problem for traditional insurance companies.At this stage,only equilibrium pricing can be carried out.Inevitably,there will be a problem of adverse selection: low-risk insured people will leave the insurance market because the equilibrium premium is higher than the maximum premium that can be measured by themselves,and ultimately the overall risk of the remaining insured population in the insurance market will increase.Then the insurance company's feedback report based on market risk is aware of the increase in risk,and has to raise the premium again because of the risk of reducing its own risk.In the long run,it will form a “vicious circle” between policyholders and insurance companies.Secondly,the P2P insurance model itself pays premiums in the form of co-insurance groups.How to charge the initial premiums for different policyholders according to different insurance experiences of each policyholder in the same group and reflect the principle of fairness in the final premium return phase so that the premiums actually paid by each policyholder are more reasonable Reflecting its own risk profile.It is also the key to the sustainability of the P2P insurance model.For the first question on how to alleviate the adverse selection problem,we hope to draw on Kahneman's Nobel Economics award-winning theory,the prospect theory,which can draw "real-life economic behavior decision-making" in a more reasonable and intuitive way than the expected utility theory.Therefore,this paper combines this theory with actuarial pricing theory to construct an actuarial model.In the new pricing formula,the probability of risk is no longer just the probability of the insurance subject's risk,but is corrected to be willing to buy the insured when facing the premium of the product and knowing that he will face the risk of loss.The probability of being willing to purchase the product and multiplying it by the risk.Therefore,in actuarial pricing,we take the insurance policy of the policyholder into consideration in the pricing model from the perspective of the insurance company,so that the premium obtained is the dynamic game equilibrium premium,which helps to alleviate the adverse selection problem caused by equilibrium pricing.The innovation in this part lies in the fact that we have improved the pricing model of predecessors on the basis of the combination of prospect theory and actuarial pricing,which makes it more practical.In the previous research,the research of the predecessors stayed on the theory.This paper constructs the mobile phone shatter-screen insurance operated by P2P insurance mode through empirical methods,and uses the parameters derived from the original experiments of Kahneman and Tversky as the control group.Compare the obtained premium with a company's mobile phone shatter-screen insurance pure premium,get the reasonableness of the premium,prove the practical operability and practical significance of the prospect theory;Find out the impact of changes in each parameter on the change in premiums.It is concluded that the existence of the ? value will produce the "probability distortion" characteristic described by the foreground theory,so that people will have a "fascination with small probability events" and will have an incentive to insure;The existence of ? value will affect people's inner measure of the equivalent loss,that is,the larger the ? value,the greater the value of the certainty in the mind,and the higher the maximum acceptable premium;According to the changes of various parameters,the changes of the policyholders' different decisions are reflected.The change of premiums represents the change of the maximum acceptable premiums of the policyholders.The comparison between the two changes reflects the fact that the prospect theory actually reflects the policyholder's decision in the acceptable premium.The research method flow for introducing the prospect theory into the actuarial pricing model is as follows: First,the derivation of the pricing formula and the construction of the model.Then,according to the original experimental procedures of Kahneman and Tversky,20 students from Southwestern University of Finance and Economics were investigated.The CE research paradigm was used to perform nonlinear regression using SPSS software to obtain various parameters.Finally,the univariate solution in the EXCEL software is used to find the corresponding premium.For the second question of how to effectively allocate premiums,we use the Shapley value method to build a game model based on previous research,and determine the expected marginal contribution of each policyholder in the coinsurance group as the premium that the insured should bear.In the second model,considering the insurance company as a commercial organization,in order to bring benefits to shareholders and maximize the company's profits,we still use the Premium for the first model,because this premium is the maximum premium that the insured is willing to accept when facing the risk.Using the premium to carry out the model calculation can not only ensure the reasonable allocation of premiums,but also meet the company's maximum profit.In the final conclusion,we will compare the characteristic premiums obtained by Shapley value to the premiums obtained by the insurance premiums when purchasing insurance separately,and compare the marginal contributions of the coinsurance group premiums.We find that the order of the feature premiums obtained by the Shapley value method is consistent with the order of the marginal contribution values of the premiums of the co-insurance group.In order to explain the problem more,after comparing the three,it is found that the participant with the higher marginal contribution value of the co-insurance group will have a characteristic premium higher than its corresponding proportional premium.The participant with the marginal contribution value of the premium will be smaller.Its characteristic premium will be less than its corresponding proportional premium.In the end,we can conclude that the insured person who has a higher marginal contribution to the overall premium should take on more assessed premiums.The insured person whose value of the marginal contribution of the overall premium is smaller should be less burdened with the premium.