Research On The Risk Pricing Of Consumer Loan With Guarantee Insurance

With the development of the economy and the integration of financial technology and consumer loans,the scale of consumer loan is gradually rising.At the same time,insurance companies begin to use their own risk control advantages to enter the field of consumer finance.As an effective tool for credit enhancement and credit risk transfer,guarantee insurance has realized the integration of the credit industry and the insurance industry.With the addition of the insurer,the original single loan interest rate pricing is extended to the double pricing of both loan interest rate and premium rate.At present,the pricing of consumer loan guarantee insurance products is controversial in the lending and insurance industry,and there is also a lack of unified pricing ideas for reference.Therefore,it is necessary and urgent to study and solve the pricing method of insurance consumer loans.This paper focuses on the measurement of repayment loss,loss risk sharing between lender and insurer,adverse selection effect,non-cooperative dynamic game optimal pricing strategy and optimization of pricing strategy under the cooperation of both sides.The main contents of this paper are as follows:Firstly,aiming at the problem of describing the repayment process of consumer loans and measuring the expected loss of repayment,the Markov model of the transition process of consumer repayment state is constructed.The relationship between the repayment state process of consumers and the accumulated outstanding instalments is derived.The analytical expressions of expected cash flow and expected loss of repayment including overdue default interest are obtained.The results show that the expected loss of consumer loan repayment first decreases and then increases,showing a downward convex shape.The higher the penalty rate,the greater the expected value of loan repayment cash flow,the smaller the expected loss rate of repayment.In the early stage of repayment,the impact of penalty interest on repayment cash flow increases,and then remains unchanged.Secondly,we price the guaranteed insurance consumer loan based on the non-cooperative dynamic game theory.Assuming that the repayment process of consumers is not affected by loan price and other factors,this paper deduces the allocation relationship between the lender and the insurer about the loss of consumer loans under complete insurance and deductible insurance based on the expected loss and the repayment cash of consumer loans.Based on this,the profit function of both parties is obtained,and the dynamic game pricing model with dominant lender is constructed.The Nash equilibrium of the game model and its numerical solution are obtained by back-induction and Fibonacci optimization methods.The results show that the expected loss of consumer loan shared by the lender and the insurer increases and decreases respectively with the increase of deductible instalments,and both are piecewise linear.The optimal loan interest rate increases,the optimal premium rate decreases,and the optimal profit of both parties decreases.In this case,the full guarantee insurance is more in line with the interests of both parties,so deductible guarantee insurance should be treated with caution.Thirdly,we study the adverse selection of consumer loans and its impact on dynamic game pricing.Considering the reverse effect of pricing and deductible clauses on the repayment process of consumers,this paper extends the effect of adverse selection in current consumer loans from price on the default probability of consumers to price and deductible instalment on the transition probability of repayment state of consumers.The solution of expected loss of repayment of consumer loans under adverse selection and its apportionment relationship between the lender and the insurer are derived.Based on this,a dynamic game model with dominant lenders under adverse selection is constructed.A nested Fibonacci optimization method is designed to obtain the Nash equilibrium numerical solution of the game model.The results show that the price sensitivity coefficient and the number of deductible periods in the adverse selection model all adversely affect the expected loss of consumer loans in a linear function.The increase in the total loan price or the decrease in the number of deductible periods will increase the adverse selection effect.The greater the expected loss of consumer loans,the greater the proportion of losses shared by the insurer,and the smaller the proportion of losses shared by the lender.The optimal profit of both parties is negatively correlated with the price sensitivity coefficient,and positively correlated with the sensitivity coefficient of the number of deductible periods.When the sensitivity coefficient is small,the optimal profit of both parties is negatively correlated with the number of deductible periods,otherwise it is positively correlated.The condition for choosing deductible guarantee insurance is that it will greatly affect the adverse selection in consumer loans.Finally,based on the cooperative game theory,the optimization of pricing strategy and incremental profit distribution are studied.According to the dynamic game pricing results of both sides under adverse selection,the cooperative game model of consumer loan with guarantee insurance is constructed.The Nash solution,K-S solution and improved K-S solution of cooperative game under different bargaining power and incremental profit distribution mechanisms are obtained by maximizing the generalized Nash product and coordinate rotation method.The results show that the cooperative game can promote the win-win among the lender,the insurer,and the consumer.The optimal pricing strategy under the cooperative game is: the loan interest rate takes the lower limit of the price constraint,and the premium rate is the solution to maximize the profit of the system.Whether the bargaining power coefficient or the distribution mechanism,it will only affect the optimal profit,but not affect the optimal pricing strategy of cooperative game.