Analysis on the credit-risk decision model with imperfect information

The research establishes a credit-risk decision model for banks with imperfect information when there are two types of applicants: one is high-risk type and the other is low-risk type. We consider two forms of the losses of the funds: the fund's loss which means that the applicants default their loan obligation, or the opportunity loss which means that the bank denies the applicants because of misjudgment. We give detail mathematical description about the two forms of the losses. In our model,the proportion of the high-risk type is larger than that of the low-risk type during the borrowers under the same rationing. The high-risk borrowers choose contracts with high collateral requirements and the low-risk borrowers choose contracts with low collateral requirements if the bank requires the two types to provide different collateral value under the the same interest rate. We also show the banks can not rise interest rate at random. In the case of that borrowers provide the different collateral value, we analysed several frequent states of mind to applicants. we discussed how banks recognize risk types of applicants by using interest rate and collateral. We got four very important conclusions, which are almost in accord with our actual life.